The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X X X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 2 X 2 X 2 X
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 0 2X 0 0 2X 2X 0 0 0 0 0 0 0 0 2X 2X 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 0 0 0
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 0 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0
0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 2X 0 2X 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 0
0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 0 2X 2X 2X 0 2X 2X 0 2X 0 0 0 2X 0 0 0 0 2X 0 2X 2X 2X 2X 0 0 0 0 2X 2X 0 2X 0 2X 2X 0 0 0 2X 2X 0 2X 0 0 0 2X 0 2X 2X 0 0
0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 0 0 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 2X 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 2X 2X 0 0 0 2X
generates a code of length 89 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+51x^84+64x^86+165x^88+512x^89+112x^90+72x^92+16x^94+25x^96+5x^100+1x^152
The gray image is a code over GF(2) with n=712, k=10 and d=336.
This code was found by Heurico 1.16 in 24.1 seconds.