The generator matrix

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

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+152x^51+225x^52+470x^53+350x^54+750x^55+496x^56+618x^57+242x^58+382x^59+140x^60+106x^61+42x^62+58x^63+31x^64+22x^65+6x^66+2x^67+2x^68+1x^84

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 0.39 seconds.