The generator matrix

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

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+21x^48+72x^49+274x^50+360x^51+270x^52+720x^53+674x^54+720x^55+258x^56+360x^57+264x^58+72x^59+22x^60+2x^62+2x^64+2x^66+2x^80

The gray image is a linear code over GF(2) with n=432, k=12 and d=192.
This code was found by Heurico 1.16 in 0.25 seconds.