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  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1  1  0  1  1  1  1  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^3+X X^3+X^2 X^2+X X^2 X^3+X^2+X  0 X^3+X X^3 X^3+X X^3+X^2 X^2+X  0 X^2+X X^3+X^2+X X^3 X^3+X^2 X^3+X X^3+X^2  X X^3 X^2+X X^2  X  0  0 X^2+X X^3+X^2+X X^2  0 X^2 X^3+X X^3+X X^3 X^3+X^2 X^2+X  0 X^3  X X^2+X X^3+X^2+X X^2  0 X^2+X X^3+X^2
 0  0 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  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  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3
 0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3
 0  0  0  0  0 X^3 X^3 X^3 X^3  0  0  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 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 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+37x^48+128x^49+64x^50+160x^51+225x^52+856x^53+229x^54+136x^55+41x^56+104x^57+23x^58+24x^59+15x^60+3x^62+1x^64+1x^98

The gray image is a linear code over GF(2) with n=424, k=11 and d=192.
This code was found by Heurico 1.16 in 0.171 seconds.