The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^75+458x^76+262x^77+657x^78+302x^79+673x^80+282x^81+560x^82+204x^83+390x^84+84x^85+62x^86+18x^87+10x^88+6x^89+1x^94+2x^96+2x^99+6x^101+2x^104

The gray image is a code over GF(2) with n=640, k=12 and d=300.
This code was found by Heurico 1.16 in 0.782 seconds.