The generator matrix

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

generates a code of length 80 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+200x^76+708x^77+632x^78+560x^79+494x^80+432x^81+253x^82+254x^83+174x^84+168x^85+97x^86+62x^87+16x^88+24x^89+17x^90+2x^92+1x^98+1x^100

The gray image is a code over GF(2) with n=640, k=12 and d=304.
This code was found by Heurico 1.16 in 0.375 seconds.