The generator matrix

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

generates a code of length 80 over Z4[X]/(X^3+2,2X) 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 0.765 seconds.