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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 X 1 X 1 2 1 0 1 1 1 1 1 X 1 1 X 1 X 1 1 X 2 X X 2 2 1 X 1
0 X 0 0 0 2 0 2 0 X X X X+2 X+2 X X 2 2 X+2 2 X+2 X X+2 0 0 X 0 X+2 2 X+2 X+2 2 2 X+2 X+2 2 2 X+2 X X 0 X+2 0 0 X+2 2 2 X 0 0 X X+2 0 X 2 2 0 0 X+2 X X+2 2 X X 0 0 2 X X+2 X 0 2 0 X 0 0 X 2 2 X+2 X X+2 0 0 X+2 X+2 2 X 2 X X X+2 2 X 0 X+2 2
0 0 X 0 0 2 X X X X+2 X 2 X+2 X 2 2 X+2 X 0 X 0 0 X 0 X+2 2 0 X+2 0 X X+2 2 X 0 X 0 0 0 X+2 X X 2 0 2 X+2 X X+2 2 0 2 X+2 2 X+2 0 X+2 2 X+2 0 0 X X X+2 0 2 0 X 0 2 0 X 2 2 X X 2 X 2 X+2 X 2 X+2 X X X+2 X+2 0 X X 0 X+2 2 0 X X 0 0 X
0 0 0 X 0 X X X+2 2 0 0 X+2 X X X 2 X 0 2 X+2 X 2 2 X 2 X 2 X+2 X 0 X 0 0 X+2 X+2 0 X+2 0 X 0 X+2 X X 0 2 X+2 0 2 2 X 2 X X+2 X 0 X+2 2 X+2 2 X X X X+2 0 0 X 0 0 X X+2 X 2 2 X+2 X 0 X X X 2 0 X 2 0 2 0 X 0 0 2 X+2 2 2 0 X+2 0 X+2
0 0 0 0 X X 2 X X+2 X 0 X+2 X 0 2 X X+2 X X 2 0 2 0 X 0 X+2 X 0 2 X+2 X+2 2 0 0 0 0 0 X+2 X X X X X+2 X 2 0 X 2 2 X+2 2 X+2 X+2 2 2 2 X X+2 X+2 0 X 0 0 2 2 X X X+2 X+2 2 0 X 2 X+2 X+2 X 0 X X 0 2 2 X 0 0 2 X+2 X+2 X+2 2 2 X+2 X 0 X 0 X+2
generates a code of length 97 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 89.
Homogenous weight enumerator: w(x)=1x^0+32x^89+94x^90+92x^91+113x^92+122x^93+171x^94+212x^95+169x^96+214x^97+169x^98+138x^99+140x^100+94x^101+57x^102+46x^103+36x^104+34x^105+35x^106+10x^107+15x^108+8x^109+12x^110+14x^111+6x^112+8x^113+5x^114+1x^162
The gray image is a code over GF(2) with n=388, k=11 and d=178.
This code was found by Heurico 1.16 in 0.995 seconds.