The generator matrix

 1  0  0  1  1  1  0 X^3  0 X^2  1  1  1  1 X^3+X  1 X^3+X  1  1  1 X^3+X^2+X X^2+X X^3+X  X  1  1  1  1 X^3+X^2 X^3+X  1  1  X  1  1 X^3 X^2  1  1  1  1  1  1  1  1  1  1 X^3 X^3+X X^3+X X^3+X^2 X^3+X  1  1
 0  1  0  0 X^2+1 X^3+X^2+1  1 X^2+X  1  1 X^3  0 X^3+1 X^3+1 X^3+X^2+X  X  1  X X+1 X^2+X+1  1 X^2  1  1 X^2 X^2+X X^3+X^2 X^3+X^2+X+1  1  1 X^3+X^2+X+1 X^3+1  1  X X^3+X^2+1 X^2+X  1 X^3+X+1 X+1 X^3+X^2+X X^3+X^2+X+1 X+1 X^3  X X^3+X  1 X^3+X^2  1  1  1  1  0 X^2+X+1 X^3+X^2
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^3+X^2+X  1 X^2+X X^2+1  X X^2+1  1 X^2+X+1 X^3+X X^3+X X^3 X^3+X+1 X^3  1 X^2+1 X+1 X^2+X+1  1 X^2+X  1 X^3+X^2  1 X^3+X+1  0 X^3+X^2 X^3+1 X^3+1  1 X+1 X^3 X^2+X X^3+X X^3+X^2+1 X^3+X^2  1 X^3+1  0 X^2+1 X^2+X+1  X  1 X+1 X^3+X^2+1  1 X^3+X X^3+X^2+X
 0  0  0 X^2 X^2  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3 X^3  0 X^3+X^2 X^3+X^2 X^3  0  0 X^3+X^2 X^3 X^3+X^2 X^2 X^2  0 X^3+X^2  0 X^3 X^2  0 X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3  0 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3+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+374x^49+847x^50+1744x^51+1852x^52+2624x^53+2129x^54+2370x^55+1541x^56+1474x^57+789x^58+354x^59+106x^60+100x^61+19x^62+40x^63+12x^64+4x^65+2x^67+2x^71

The gray image is a linear code over GF(2) with n=432, k=14 and d=196.
This code was found by Heurico 1.16 in 3.3 seconds.