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

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

Homogenous weight enumerator: w(x)=1x^0+32x^81+6x^82+16x^83+6x^84+1x^86+1x^88+1x^94

The gray image is a code over GF(2) with n=324, k=6 and d=162.
This code was found by Heurico 1.16 in 0.354 seconds.