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  0  1  1  1  1  1  1  1  2  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  X X^2+2 X^2+2  0  2  X  X
 0  X  0  X  0  0  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X  0  0  X  X  0  0  X  X X^2  2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X  2  2  2 X+2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2  2  2 X+2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2  2  2 X+2 X+2  2  2 X+2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2  0  0  X  X X^2 X^2 X^2+X X^2+X X^2+X X^2+X+2  X  X  X  X  X X+2
 0  0  X  X X^2+2 X^2+X X^2+X+2 X^2 X^2 X^2+X X+2  2 X^2+X+2  2 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+2  X  X X^2+X+2  0  0 X^2+X  X X^2  X  2 X^2+X+2 X+2 X^2+2 X^2+2 X+2 X^2+X+2  2 X^2  X X^2+X  0  0 X^2+X  X X^2  0 X^2+X  X X^2 X^2+2 X+2 X^2+X+2  2 X^2  X X^2+X  0  2 X^2+X+2 X+2 X^2+2  0 X^2+X  X X^2 X^2+2 X+2 X^2+X  0  2 X^2 X^2+X X^2+X+2  0  2 X^2  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+328x^80+416x^82+232x^84+32x^86+14x^88+1x^144

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 0.422 seconds.