The generator matrix

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

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+158x^49+217x^50+408x^51+413x^52+656x^53+564x^54+592x^55+411x^56+290x^57+118x^58+124x^59+55x^60+48x^61+12x^62+28x^63+1x^82

The gray image is a linear code over GF(2) with n=432, k=12 and d=196.
This code was found by Heurico 1.16 in 0.36 seconds.