The generator matrix

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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+230x^80+104x^81+440x^82+160x^83+485x^84+188x^85+472x^86+124x^87+474x^88+192x^89+406x^90+152x^91+251x^92+92x^93+182x^94+12x^95+57x^96+14x^98+26x^100+18x^102+5x^104+4x^106+5x^108+1x^116+1x^120

The gray image is a code over GF(2) with n=348, k=12 and d=160.
This code was found by Heurico 1.16 in 2.21 seconds.