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

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

Homogenous weight enumerator: w(x)=1x^0+6x^76+134x^77+26x^78+264x^79+180x^80+244x^81+36x^82+104x^83+4x^84+22x^85+1x^88+1x^90+1x^130

The gray image is a code over GF(2) with n=640, k=10 and d=304.
This code was found by Heurico 1.16 in 0.563 seconds.