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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+68x^71+115x^72+158x^73+213x^74+208x^75+269x^76+308x^77+279x^78+348x^79+381x^80+304x^81+255x^82+252x^83+228x^84+184x^85+146x^86+94x^87+88x^88+46x^89+29x^90+42x^91+28x^92+20x^93+3x^94+10x^95+7x^96+4x^97+3x^98+2x^99+2x^100+1x^116

The gray image is a code over GF(2) with n=320, k=12 and d=142.
This code was found by Heurico 1.16 in 1.83 seconds.