The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+56x^48+118x^49+297x^50+508x^51+640x^52+702x^53+745x^54+770x^55+741x^56+780x^57+690x^58+622x^59+516x^60+384x^61+278x^62+142x^63+81x^64+54x^65+29x^66+6x^67+12x^68+10x^69+9x^70+1x^72

The gray image is a linear code over GF(2) with n=224, k=13 and d=96.
This code was found by Heurico 1.16 in 2.81 seconds.