The generator matrix

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

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+126x^48+128x^49+459x^50+368x^51+724x^52+544x^53+693x^54+384x^55+422x^56+96x^57+93x^58+16x^59+34x^60+3x^62+1x^64+1x^68+1x^72+1x^76+1x^80

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 0.234 seconds.