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

generates a code of length 56 over Z2[X]/(X^4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+124x^51+252x^52+346x^53+467x^54+662x^55+597x^56+638x^57+373x^58+240x^59+118x^60+114x^61+79x^62+42x^63+24x^64+6x^65+8x^66+4x^67+1x^90

The gray image is a linear code over GF(2) with n=448, k=12 and d=204.
This code was found by Heurico 1.16 in 0.375 seconds.