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

generates a code of length 80 over Z4[X]/(X^2+2) 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 37.9 seconds.