The generator matrix

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

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+142x^48+984x^49+1655x^50+2834x^51+4076x^52+4640x^53+4743x^54+4628x^55+3489x^56+2696x^57+1465x^58+806x^59+320x^60+156x^61+93x^62+20x^63+10x^64+4x^65+4x^66+2x^68

The gray image is a linear code over GF(2) with n=432, k=15 and d=192.
This code was found by Heurico 1.16 in 8.01 seconds.