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

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

Homogenous weight enumerator: w(x)=1x^0+32x^81+14x^82+10x^84+6x^86+1x^88

The gray image is a code over GF(2) with n=648, k=6 and d=324.
This code was found by Heurico 1.16 in 0.344 seconds.