The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+137x^80+132x^81+252x^82+156x^83+217x^84+124x^85+188x^86+104x^87+181x^88+112x^89+124x^90+92x^91+92x^92+44x^93+40x^94+17x^96+4x^97+16x^98+7x^100+4x^102+2x^104+1x^112+1x^120

The gray image is a code over GF(2) with n=344, k=11 and d=160.
This code was found by Heurico 1.16 in 0.736 seconds.