The generator matrix

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

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+92x^49+178x^50+542x^51+197x^52+846x^53+413x^54+846x^55+193x^56+526x^57+155x^58+82x^59+7x^60+2x^61+2x^62+2x^63+2x^64+6x^65+2x^66+1x^78+1x^82

The gray image is a linear code over GF(2) with n=432, k=12 and d=196.
This code was found by Heurico 1.16 in 0.297 seconds.