The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  1  1  1 X^2  1  1  X  1 X^2 X^2  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3  0 X^2 X^3+X^2 X^2  0 X^2 X^2 X^3+X^2  0 X^3 X^2 X^3 X^2 X^3 X^2 X^2 X^3 X^3+X^2  0 X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^2 X^3 X^3+X^2 X^2  0
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^2  0 X^3+X^2 X^3 X^3 X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^2 X^2 X^3+X^2  0 X^3  0  0 X^3 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3  0 X^3+X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2 X^2  0 X^2  0 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3 X^2 X^2  0 X^3+X^2 X^3 X^3 X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0  0 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 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+26x^48+46x^49+51x^50+104x^51+219x^52+384x^53+468x^54+372x^55+185x^56+68x^57+36x^58+24x^59+13x^60+8x^61+15x^62+12x^63+4x^64+6x^65+5x^66+1x^94

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 0.219 seconds.