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.