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  1  1  1  1  1  X  1  1  1  1  1 X^2  1  1  1  1  1 X^2  1 X^2 X^2
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^2  0 X^3 X^3+X^2 X^2 X^3+X^2 X^2  0 X^3  0 X^3 X^3+X^2 X^2  0 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^2  0  0 X^3 X^3  0 X^3 X^3+X^2 X^2 X^3 X^2 X^2 X^3+X^2  0 X^3 X^3 X^2  0 X^3
 0  0 X^3  0  0  0  0  0 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3
 0  0  0  0 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0
 0  0  0  0  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0  0  0  0  0 X^3 X^3  0  0  0  0 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+132x^48+32x^49+64x^50+128x^51+86x^52+1216x^53+64x^54+128x^55+88x^56+32x^57+56x^60+18x^64+2x^68+1x^96

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 0.203 seconds.