The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  1  1  1  X  1  1  1  1  X  1  0  1 X^3  1  1  1  1  1  1  1  1  1  1 X^2  X X^3  1  1  X X^2  1  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^3 X^2+X  0 X^2+X X^2 X^3+X X^2  X X^2+X  X X^3+X^2+X X^2 X^3+X^2+X X^2  0 X^3+X^2+X  X X^3+X^2+X  0 X^2+X X^2  X X^2+X X^3+X  X X^3  X X^3+X  0 X^3+X^2+X  0 X^2+X X^2 X^3  X X^2+X X^2+X X^3 X^2+X  X X^3+X^2 X^3+X X^3+X^2+X X^3+X^2 X^2+X  0
 0  0 X^3+X^2  0 X^2  0  0 X^3  0 X^2 X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2  0 X^2 X^2  0 X^2 X^3 X^2 X^2 X^2  0 X^3 X^2  0 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^3 X^3 X^3  0  0  0 X^2 X^2 X^2 X^2  0
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^2 X^2 X^2 X^3 X^3+X^2  0 X^2 X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3 X^3  0 X^3 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2  0 X^3 X^3  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2  0
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  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+114x^48+98x^49+267x^50+166x^51+610x^52+388x^53+883x^54+402x^55+568x^56+138x^57+242x^58+56x^59+100x^60+16x^61+12x^62+10x^63+13x^64+3x^66+6x^67+2x^68+1x^86

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 0.438 seconds.