The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  0  1  1  1  X  1  1 X^3+X^2  1  1 X^3  X  1  X  1  0  1 X^2  1  1 X^3 X^3 X^3 X^3  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X  0 X^2+X X^3 X^2+X X^3+X X^2 X^2  X  0 X^2+X X^3+X^2+X  X X^2 X^3 X^3 X^3+X  X  X X^3+X^2  0  X X^2+X  X X^3 X^2+X X^3 X^3+X^2+X  X X^3+X^2 X^2+X  X X^2+X X^2  0  0  X X^3+X  0 X^2  X  X  X  X X^2 X^3+X
 0  0 X^3+X^2  0 X^2  0 X^3  0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3  0 X^3+X^2  0 X^3 X^2 X^2 X^2 X^3  0 X^3+X^2  0  0 X^3 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3
 0  0  0 X^3+X^2  0 X^3 X^3 X^2 X^2 X^2 X^2  0  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0  0 X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^2 X^3 X^3 X^2 X^3  0  0 X^2  0 X^3 X^3 X^2  0 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3+X^2 X^2  0 X^3+X^2 X^2 X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  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+263x^48+64x^49+576x^50+176x^51+770x^52+528x^53+706x^54+208x^55+478x^56+48x^57+174x^58+74x^60+14x^62+9x^64+2x^66+4x^68+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 123 seconds.