The generator matrix

 1  0  1  1  1  2  1  1  0  0  1  1  1  0  1  1  2  1  1  1  2  1  1  0  1  2  1  1  X  1  2  1  1  1  1  1  0  1  1  1  X  1  1  1  X  1  1  1  1 X+2 X+2  1  X  X  1  0  X  1  0  X X+2  1  1  2  0  1  1  2 X+2  1  1  0  1  1  1  1  0  1  1  2 X+2  X  1  1  1  1  1  X  1
 0  1  1  0  1  1  2 X+1  1  1  2 X+3  2  1  3  2  1 X+3 X+2  1  1  2 X+1  1  2  1 X+3 X+2  1  1  1  3 X+2 X+3  0  X  1  X X+1  3  1  1  0 X+3  1  X  X X+1  1  1  1  2  1  1  0  1  1  0  1  1  1  0  0  1  1 X+1  X  1  1  3  1  1 X+3  X X+1 X+3  1 X+1  3  X  1  1  0  2 X+2  X  1  X  0
 0  0  X  0  0  0  0  2 X+2  X X+2 X+2 X+2  2  0 X+2  X X+2  0 X+2  2  X  2 X+2  2  2  2 X+2  2  X X+2 X+2 X+2  2  X  X  0  2  0  0  2  X  X X+2 X+2  0 X+2  0  X  X  X  2  2  X  2  2  0  X  2 X+2  X  2  X X+2 X+2  X X+2  X  2  2 X+2 X+2  2 X+2  X X+2  X X+2 X+2  X  X  X X+2  2  2  X  0  2  0
 0  0  0  X  0  0  2  2  2  2  0  2  2 X+2  X X+2 X+2  X X+2 X+2  X  X  X X+2 X+2  X  0  0 X+2  0  0  2  0  X  2  X X+2  X  X X+2  0  X  X  X  0  2  0  X  2 X+2  0  2  X  0 X+2  0 X+2 X+2  2  2 X+2  X  2  X  0 X+2  X X+2  0 X+2  2 X+2  0  X  2 X+2  2  0  2  0  2  2  0  2  X  0  2  2  0
 0  0  0  0  X X+2 X+2  2  X  0  0 X+2  X  X  X X+2  2  X  X  2  0  2  2  X X+2  X  X  0  0  X  2  0  X  X  0  X  X  0  2 X+2  2 X+2  X  2 X+2  X X+2  X  X  0 X+2  0  0  2  2  2 X+2  2 X+2  0 X+2  X  2 X+2 X+2 X+2 X+2  0 X+2  2 X+2  2 X+2  0  0  0 X+2  X  2 X+2  X  2  X  X  X  0  0  X  2

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+60x^81+154x^82+250x^83+244x^84+334x^85+350x^86+264x^87+310x^88+302x^89+316x^90+264x^91+292x^92+318x^93+209x^94+138x^95+121x^96+64x^97+14x^98+24x^99+13x^100+10x^101+11x^102+6x^104+14x^105+2x^106+2x^107+2x^109+2x^111+3x^112+1x^116+1x^120

The gray image is a code over GF(2) with n=356, k=12 and d=162.
This code was found by Heurico 1.16 in 1.57 seconds.