The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0 X^2  1  1  1  1 X^2+X+2  X X+2  1  1  1  1  X X^2+X+2 X^2  2  1 X^2+X+2  1  1  1  1  1 X^2+2  1  1 X^2+X  1  1  1  1  1  1 X^2+2  0  X  X X^2  X  1 X^2+X
 0  1  0  2 X^2+1 X^2+3  1  0 X^2+1  1  2 X^2+3  1  X X+2  X X^2+X+3 X^2+X+1 X^2+2  1  1 X+3 X^2+X+2 X+1 X^2+X X^2+X  1 X^2  1  0  1 X+1 X^2+X+3  1  3 X^2+2  1 X^2  X  1 X^2+3 X^2+1 X^2+X+3  1 X^2+X+3 X^2+X+2 X^2+X+2 X^2 X+2  1  0 X^2 X^2+X+3  1
 0  0  1 X+3 X+1  2 X^2+X+1 X^2+X X^2+1  3 X^2+3 X^2+X+2 X^2+X+2  1 X+2 X^2+3 X+1  X  1 X^2+X+1  X  2 X+3  1 X^2  1 X+1  1 X+3 X^2+X+3 X^2+2 X^2+X+1  2 X^2+2 X^2+1 X^2+X+3  3 X^2+2 X+1  3  1 X^2+X+1  1  0 X^2+X  0  1  1  1 X^2+X+2  1  1 X^2+1 X+2

generates a code of length 54 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+616x^51+731x^52+644x^53+662x^54+418x^55+328x^56+302x^57+174x^58+106x^59+18x^60+86x^61+4x^62+4x^63+1x^64+1x^68

The gray image is a code over GF(2) with n=432, k=12 and d=204.
This code was found by Heurico 1.16 in 139 seconds.