The generator matrix

 1  0  0  1  1  1  2  2 2X+2  1  1  2  1  1 3X  1  1 3X  X  1  1  1 X+2 3X+2  1  1  1 3X+2  1  2  1 2X  1 2X 3X+2  1 2X+2 3X  1  1 2X+2  1  1  1 3X+2  X  0  1  0  1  1 2X  1  1 X+2  1 X+2 3X  1  1  1 3X+2  X  1  2  1  1  1 2X+2  X  1  2 2X+2 X+2  2 2X+2 2X X+2  X  1
 0  1  0  0  3  3  1  X  1 2X 2X+3  1  2  1 3X+2 3X 3X+3  1  1 3X+3 3X+2 3X+1  1 2X+2 X+1 X+2  X  1  2 2X 3X+3 3X  1  1  1 2X  1  1 X+3 3X+2  1  X  3 2X+3  1  1  1 3X  1 3X+3  0 2X+2 3X+3  2 3X+2 3X+2  1  0  X  3 3X  1 X+2  3 3X+2 2X+2  1 2X  1  1 3X+1 X+2 2X  1  1  1 2X+2 X+2  1  0
 0  0  1 X+1 3X+1 2X 3X+3  1 3X  X 3X  3  3 2X+3  1  1  2  3 3X 2X+1  X 3X+1  0  1  2 X+1  0 3X+3  1  1 X+3  1 2X+2 2X  3 3X+3 X+2  0  X X+2 3X+3 2X+3 2X+1 3X+2 3X+2 X+3  1 3X+3 3X+2 X+2  2  1  3  X  1  0 2X+2  1 2X+2 3X+3  1  X  1 2X+3  1 X+3 3X+1 2X  0 2X+2 X+2  1  1  X 2X+2 2X+1  1  1 2X+3  0
 0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X  0  0 2X  0 2X  0 2X  0  0  0  0  0  0  0 2X  0 2X  0 2X  0 2X 2X  0  0 2X  0  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+204x^75+649x^76+1028x^77+1108x^78+1138x^79+892x^80+798x^81+737x^82+506x^83+348x^84+306x^85+195x^86+128x^87+93x^88+44x^89+6x^90+4x^91+1x^92+4x^95+1x^98+1x^102

The gray image is a code over GF(2) with n=640, k=13 and d=300.
This code was found by Heurico 1.16 in 1.09 seconds.