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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+18x^80+28x^81+47x^82+332x^83+46x^84+18x^85+8x^86+4x^87+7x^88+1x^98+2x^117

The gray image is a code over GF(2) with n=664, k=9 and d=320.
This code was found by Heurico 1.16 in 0.625 seconds.