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

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+44x^49+140x^50+92x^51+97x^52+440x^53+434x^54+440x^55+82x^56+92x^57+128x^58+44x^59+10x^60+2x^62+1x^64+1x^100

The gray image is a linear code over GF(2) with n=432, k=11 and d=196.
This code was found by Heurico 1.16 in 0.188 seconds.