The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1  1 X^2  1  1  1  1  0  1  1  1  X  1  1  1  1  X  1  2 X^2  1  1  1  1 X^2+2 X+2  0  1  1 X^2+X+2  1  1  1  1  1 X^2+2  1  1  2  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3  1  2 X^2+1 X^2+X+3  X  1 X+2 X^2+1 X^2+1  1 X+3 X+1  2 X^2+X+1  1 X^2+X+2  1  1  1 X^2+X+1 X+3  1  1  1  1 X^2+X+2  2  1 X^2+2 X^2 X^2+X+1 X^2+X X^2+X X^2 X^2+X+3  3 X^2+2  0
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2+2 X^2 X^2+X+2 X^2+2 X+2 X^2+2 X^2+X+2  2 X^2 X^2+X X^2+X  0 X+2  0  X X^2 X+2 X^2+X X^2+X+2  X X^2+2 X^2+X+2 X^2 X^2+2 X^2+X X^2+X  2 X^2+2  X X^2 X^2+X+2 X+2 X^2  2 X^2 X^2+X+2  0  X X^2 X+2  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+206x^51+566x^52+244x^53+193x^54+184x^55+388x^56+164x^57+13x^58+26x^59+52x^60+8x^61+1x^66+1x^70+1x^72

The gray image is a code over GF(2) with n=432, k=11 and d=204.
This code was found by Heurico 1.16 in 0.109 seconds.