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

generates a code of length 91 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+171x^80+4x^81+304x^82+28x^83+513x^84+132x^85+578x^86+256x^87+798x^88+344x^89+790x^90+472x^91+899x^92+440x^93+644x^94+224x^95+528x^96+100x^97+348x^98+44x^99+262x^100+4x^101+122x^102+107x^104+30x^106+35x^108+9x^112+3x^116+1x^120+1x^128

The gray image is a code over GF(2) with n=364, k=13 and d=160.
This code was found by Heurico 1.16 in 9.39 seconds.