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

generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+20x^83+5x^84+4x^85+2x^86

The gray image is a code over GF(2) with n=648, k=5 and d=332.
This code was found by Heurico 1.16 in 0.343 seconds.