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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+36x^82+192x^83+12x^84+8x^86+1x^88+4x^90+1x^104+1x^112

The gray image is a code over GF(2) with n=664, k=8 and d=328.
This code was found by Heurico 1.16 in 12.4 seconds.