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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2+2  X  0  X X^2+2  X  0  X  X  0  X  2  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X+2 X^2+2  0 X^2+X X^2+2  X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2 X+2  2 X^2+X X^2  X X^2+X+2  0 X+2 X^2+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2  X X^2+X  X X+2  X X^2+X  X X+2  X X^2+X  X X+2  0  X  0 X^2  0
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  0  0  2  2  0  0  0  0  2  0  0  2  2  2  2  2  2  0  2  0  2  0  0  0  2  2  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  0  2  0  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  2  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  0  0  2  2  2  0  0  0  0  2  2  2  0  0  2  2  2  0  2  0  0  2  0  2  0  0  2  0  0  2  2  2  2  0  0  0  0  2  2  0  0  2  0
 0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  2  2  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  0  0  2  0  0  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+6x^76+134x^77+26x^78+264x^79+180x^80+244x^81+36x^82+104x^83+4x^84+22x^85+1x^88+1x^90+1x^130

The gray image is a code over GF(2) with n=640, k=10 and d=304.
This code was found by Heurico 1.16 in 0.547 seconds.