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 X^3+X^2  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1 X^3+X^2  X  0  0  X  1  X  1 X^2  1  X  X  1
 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^3 X^2+X X^3+X X^3+X^2+X  X X^2+X X^2 X^3+X X^3+X X^3+X^2 X^3+X^2 X^3+X X^2+X X^3+X^2+X  X X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  X  X  0  0 X^3+X^2+X X^3+X X^2+X  X X^3+X^2+X X^3+X X^2+X  0
 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 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2  X X^2+X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2  X X^3+X^2+X X^2 X^3+X^2  X  0  0  X  0 X^3  X  X X^3+X^2 X^3+X^2 X^2+X X^2+X X^3+X X^3+X^2 X^2+X X^2
 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^2 X^3 X^3 X^2  0 X^3+X^2 X^3 X^3  0 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^2 X^2  0 X^2 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+119x^48+220x^49+427x^50+492x^51+566x^52+606x^53+610x^54+364x^55+276x^56+176x^57+116x^58+36x^59+46x^60+22x^61+14x^62+4x^63+1x^82

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 0.344 seconds.