The generator matrix

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

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+148x^75+330x^76+504x^77+492x^78+416x^79+462x^80+424x^81+433x^82+376x^83+272x^84+116x^85+46x^86+46x^87+7x^88+12x^89+1x^90+2x^91+2x^98+2x^99+2x^103+2x^106

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 0.766 seconds.