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

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+156x^80+248x^82+70x^84+8x^86+24x^88+2x^92+1x^96+2x^104

The gray image is a code over GF(2) with n=656, k=9 and d=320.
This code was found by Heurico 1.16 in 0.578 seconds.