The generator matrix

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

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+386x^76+552x^77+583x^78+384x^79+506x^80+392x^81+459x^82+384x^83+272x^84+64x^85+65x^86+8x^88+8x^89+9x^90+4x^92+8x^93+4x^94+5x^96+1x^100+1x^116

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 0.781 seconds.