The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+80x^81+226x^82+298x^83+445x^84+288x^85+451x^86+364x^87+354x^88+214x^89+285x^90+208x^91+210x^92+144x^93+147x^94+90x^95+96x^96+62x^97+35x^98+26x^99+43x^100+12x^101+2x^102+6x^103+6x^106+2x^108+1x^112

The gray image is a code over GF(2) with n=352, k=12 and d=162.
This code was found by Heurico 1.16 in 1.46 seconds.