The generator matrix

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

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+38x^48+64x^49+54x^50+76x^51+22x^52+512x^53+538x^54+488x^55+38x^56+100x^57+38x^58+12x^59+26x^60+24x^61+6x^62+3x^64+4x^65+3x^66+1x^98

The gray image is a linear code over GF(2) with n=432, k=11 and d=192.
This code was found by Heurico 1.16 in 0.203 seconds.