The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  1  X  X  1  1  0  1  1  0  1  1 X+2  1  1  1  1  1  2  1 X+2  1  1  1  1  2  1  1  1  X  2  1  X  2  1  1  X  1  1  1  1  1  1  1  1 X+2 X+2  2  1  1  X  2  2  0  1  2  X  1  1  1  1  1  1  1  1  1  2  1
 0  1  1  0 X+3  1 X+1 X+2  1  2  3  1  X X+3  1  1  1 X+2  1  1  X  1  0 X+1  1 X+2  1  2 X+1  3  1 X+1  1  X  1  0 X+3  1  X  1  2  1  1  X  1  1 X+3  2  1  1  3  0 X+3  2  1  X  0  1  1  1 X+1  2  0  1  1  1 X+2  1 X+2  1  0 X+2 X+1 X+3 X+2 X+3 X+1  2  X  0
 0  0  X  0 X+2  0  2  2  X X+2  0 X+2 X+2  2  0  X X+2 X+2 X+2  2  0  0  X X+2 X+2  0  2 X+2  2  0 X+2  2  2  X  X  0  X  0  X  2  0  0  0  X X+2  0 X+2  0 X+2  X  2  X X+2  0  0  X  X  X  2 X+2 X+2  X  2  0  2  2 X+2 X+2 X+2  X X+2 X+2  X  2  2  2  X  2  2  0
 0  0  0  X  0  0  0  2  2  2  2  0  2 X+2 X+2  X X+2 X+2  X X+2 X+2  X X+2 X+2 X+2  2  X  2 X+2  0  0  0  0  X  2  2 X+2 X+2  0  2 X+2  X X+2 X+2  0  0  X  0  0  X  0 X+2  0  0  2  2  X X+2 X+2  2  0 X+2  X  0  X X+2  0 X+2  2  2  X X+2  X  2  2  0  0 X+2 X+2  0
 0  0  0  0  2  0  0  0  2  2  0  2  2  0  0  2  2  2  2  0  0  0  2  0  0  2  2  0  2  2  0  2  2  0  0  2  0  2  0  2  2  0  2  0  0  0  2  2  0  2  2  0  0  0  0  2  0  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  0  0  0  0  0  0  0
 0  0  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  2  2  0  0  0  0  2  0  2  2  0  0  2  0  0  2  2  2  2  0  2  2  0  0  2  2  2  0  0  0  2  0  0  0  2  2  0  2  0  0  0  2  2  2  2  2  2  2  2  2  0  2  0  0  0  0  0  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+52x^72+160x^73+151x^74+322x^75+256x^76+394x^77+253x^78+490x^79+211x^80+362x^81+224x^82+388x^83+187x^84+248x^85+102x^86+124x^87+42x^88+44x^89+17x^90+14x^91+10x^92+6x^93+14x^94+2x^95+6x^96+2x^97+3x^98+4x^99+3x^100+3x^102+1x^106

The gray image is a code over GF(2) with n=320, k=12 and d=144.
This code was found by Heurico 1.16 in 1.4 seconds.