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

generates a code of length 80 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+82x^75+75x^76+154x^77+123x^78+212x^79+760x^80+212x^81+123x^82+154x^83+57x^84+82x^85+9x^86+3x^88+1x^154

The gray image is a code over GF(2) with n=640, k=11 and d=300.
This code was found by Heurico 1.16 in 6.7 seconds.