The generator matrix

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

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+650x^51+511x^52+1074x^53+300x^54+620x^55+190x^56+372x^57+112x^58+162x^59+32x^60+58x^61+4x^62+8x^63+1x^64+1x^68

The gray image is a linear code over GF(2) with n=432, k=12 and d=204.
This code was found by Heurico 1.16 in 79.8 seconds.