The generator matrix

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

generates a code of length 56 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+43x^50+166x^51+154x^52+470x^53+262x^54+774x^55+374x^56+858x^57+293x^58+368x^59+89x^60+134x^61+33x^62+32x^63+16x^64+6x^65+8x^66+2x^67+5x^68+4x^69+1x^70+2x^71+1x^88

The gray image is a linear code over GF(2) with n=448, k=12 and d=200.
This code was found by Heurico 1.16 in 0.469 seconds.