The generator matrix

 1  0  0  1  1  1  2  0  1  1  1  1  2  2  1  1  0  1  1 X+2  0  1  1  X  1  1 X+2  0  1  1  1 X+2  2  1  0  1  0  1  1  1  X  X  1 X+2  1  X  2  1 X+2  0  1  X  0  1  1 X+2  1  0  1  1  1  X  1  1  2  X X+2  X  1  X X+2  1  X  X  1  1  1  1 X+2  1
 0  1  0  0  1  1  1  2  2  0  3  1  1  1  0  1  1  X X+3  1 X+2 X+2 X+1  1  2  1  2  1  1  3  0  X  1  0  1  3 X+2  X X+3 X+2  1  0  X  1  3  1  1 X+1  1  1 X+3  1 X+2  X  X  0 X+1  1  3 X+1  3  1 X+3  2  1  1  1  1 X+3 X+2  X  1  1  1  3  2 X+1  3  1  0
 0  0  1  1  2  3  1  1  0  1  2  3  3  2 X+1 X+3  X  2  X  1  1 X+2  0 X+3 X+1  1  1  X X+2 X+3  X  1 X+1  3  2 X+3  1  0  X  3  1  1 X+1 X+1 X+2  0 X+1  3  0  X  1 X+1  1  1 X+3  1  1  0 X+1 X+3  X  2  X  X X+1 X+2  0  X X+1  1  1  0 X+2 X+2  X X+2  1  1 X+3  0
 0  0  0  X  0  X  X  X  X  2  X  2  0 X+2  X  X  0 X+2 X+2  0 X+2 X+2 X+2  0  2 X+2 X+2 X+2  0  0  0 X+2  X X+2  2  2  0  2  0  2 X+2  2  X  X  X  2  2  0 X+2  X X+2 X+2  X  X  2  X  X X+2 X+2  0  2  X  X X+2 X+2  X  0 X+2 X+2  X  2  X X+2  2 X+2 X+2  2 X+2 X+2  0

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+29x^74+138x^75+248x^76+262x^77+214x^78+214x^79+215x^80+156x^81+91x^82+88x^83+87x^84+44x^85+49x^86+58x^87+55x^88+46x^89+15x^90+10x^91+17x^92+2x^93+4x^95+1x^96+2x^97+1x^98+1x^102

The gray image is a code over GF(2) with n=320, k=11 and d=148.
This code was found by Heurico 1.11 in 0.343 seconds.