The generator matrix

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

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+72x^81+337x^82+414x^83+716x^84+610x^85+762x^86+594x^87+617x^88+530x^89+663x^90+470x^91+595x^92+328x^93+355x^94+254x^95+320x^96+162x^97+138x^98+110x^99+77x^100+26x^101+15x^102+12x^103+10x^104+2x^106+2x^107

The gray image is a code over GF(2) with n=356, k=13 and d=162.
This code was found by Heurico 1.13 in 1.98 seconds.