The generator matrix

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

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+107x^76+192x^77+486x^78+64x^79+428x^80+64x^81+380x^82+192x^83+97x^84+30x^86+1x^88+4x^100+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 0.594 seconds.