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

generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+270x^80+512x^82+224x^84+16x^88+1x^160

The gray image is a code over GF(2) with n=656, k=10 and d=320.
This code was found by Heurico 1.16 in 44.9 seconds.