The generator matrix

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

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+30x^48+240x^49+417x^50+550x^51+627x^52+528x^53+551x^54+488x^55+343x^56+212x^57+47x^58+16x^59+21x^60+8x^61+9x^62+4x^65+2x^67+2x^72

The gray image is a linear code over GF(2) with n=424, k=12 and d=192.
This code was found by Heurico 1.16 in 0.235 seconds.