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

generates a code of length 56 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+35x^48+29x^50+43x^52+32x^53+28x^54+352x^55+1040x^56+352x^57+28x^58+32x^59+14x^60+20x^62+10x^64+13x^66+7x^68+7x^70+2x^72+2x^74+1x^102

The gray image is a linear code over GF(2) with n=448, k=11 and d=192.
This code was found by Heurico 1.16 in 0.203 seconds.