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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2  2 X^2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2  0  2  0  2  0  2  0  2 X^2  0  2 X^2  0  2 X^2 X^2  0  2 X^2 X^2 X^2 X^2  0  2 X^2+2 X^2  0  2 X^2+2 X^2  0  0  2  2 X^2+2 X^2+2 X^2+2 X^2  0 X^2+2 X^2+2  0  0
 0  0  2  0  0  0  2  0  0  2  0  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  2  2  2  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  0  0  2  0  2  2  0  0  2  0  2  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  2  2  2  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  0  2  0  0  0  0  0  2  2  2  2  0  0  0  0  2  0  0  2  0  2  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+17x^80+28x^81+22x^82+398x^83+12x^84+16x^85+3x^86+2x^88+4x^89+6x^90+1x^102+2x^115

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 0.609 seconds.