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

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+38x^72+72x^73+82x^74+112x^75+117x^76+150x^77+173x^78+218x^79+253x^80+186x^81+165x^82+126x^83+68x^84+78x^85+60x^86+34x^87+24x^88+16x^89+23x^90+20x^91+11x^92+8x^93+6x^94+2x^97+2x^98+2x^99+1x^134

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 0.719 seconds.