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

generates a code of length 80 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+180x^76+80x^77+296x^78+384x^79+377x^80+272x^81+184x^82+32x^83+148x^84+64x^86+29x^88+1x^152

The gray image is a code over GF(2) with n=640, k=11 and d=304.
This code was found by Heurico 1.16 in 37.8 seconds.