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

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+174x^50+364x^51+392x^52+650x^53+719x^54+700x^55+351x^56+256x^57+97x^58+104x^59+34x^60+54x^61+15x^62+16x^63+6x^64+2x^65+2x^66+1x^90

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 0.344 seconds.