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

generates a code of length 93 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+30x^81+100x^82+120x^83+173x^84+194x^85+264x^86+354x^87+431x^88+496x^89+545x^90+574x^91+639x^92+640x^93+587x^94+588x^95+467x^96+436x^97+353x^98+296x^99+221x^100+174x^101+126x^102+94x^103+83x^104+60x^105+49x^106+18x^107+21x^108+16x^109+15x^110+4x^111+7x^112+2x^113+8x^114+2x^116+2x^120+1x^128+1x^130

The gray image is a code over GF(2) with n=372, k=13 and d=162.
This code was found by Heurico 1.16 in 13.4 seconds.