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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+34x^72+82x^73+93x^74+124x^75+136x^76+152x^77+181x^78+194x^79+163x^80+180x^81+189x^82+132x^83+104x^84+64x^85+61x^86+40x^87+28x^88+16x^89+18x^90+16x^91+8x^92+14x^93+2x^94+6x^95+5x^96+2x^97+2x^101+1x^128

The gray image is a code over GF(2) with n=320, k=11 and d=144.
This code was found by Heurico 1.16 in 0.62 seconds.