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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+60x^80+122x^81+196x^82+338x^83+348x^84+328x^85+314x^86+252x^87+311x^88+324x^89+295x^90+306x^91+257x^92+206x^93+159x^94+104x^95+51x^96+28x^97+14x^98+18x^99+15x^100+10x^101+8x^102+4x^103+12x^104+6x^105+2x^106+2x^107+2x^110+1x^112+1x^114+1x^118

The gray image is a code over GF(2) with n=352, k=12 and d=160.
This code was found by Heurico 1.16 in 1.53 seconds.