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

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+332x^75+184x^76+412x^77+224x^78+564x^79+733x^80+576x^81+224x^82+348x^83+158x^84+272x^85+28x^87+2x^88+16x^89+8x^91+9x^92+4x^93+1x^140

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 125 seconds.