The generator matrix

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

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+244x^76+104x^77+240x^78+88x^79+692x^80+88x^81+240x^82+104x^83+244x^84+1x^96+2x^112

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 0.406 seconds.