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

generates a code of length 80 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+228x^74+350x^76+96x^77+596x^78+416x^79+827x^80+416x^81+564x^82+96x^83+256x^84+124x^86+92x^88+24x^90+9x^92+1x^140

The gray image is a code over GF(2) with n=640, k=12 and d=296.
This code was found by Heurico 1.16 in 128 seconds.