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

generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+58x^82+2x^84+2x^86+1x^88

The gray image is a code over GF(2) with n=648, k=6 and d=328.
This code was found by Heurico 1.16 in 0.422 seconds.