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  X  0  X X^2+2  X  0  X X^2+2  X  0  X X^2+2  X  X  0 X^2  2 X^2 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 X^2+2  0 X^2+X X^2+2  X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2  X  0 X^2+X X^2+2  X  0 X^2+X X^2+2 X+2  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+2 X^2 X+2  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+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 X^2+X X^2+X+2  X  0  X  0  0
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  2  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  0  0  0  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  2  0  0  0  0  2  2  2  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  2  2  2  0  0  0  0  2  2  2  0  2  0  0  0  0
 0  0  0  0  2  2  2  2  2  0  2  0  0  2  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  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  0  0  2  0  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+356x^80+160x^82+216x^84+224x^86+56x^88+8x^92+2x^96+1x^128

The gray image is a code over GF(2) with n=664, k=10 and d=320.
This code was found by Heurico 1.16 in 0.641 seconds.