The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+131x^50+260x^51+316x^52+432x^53+453x^54+416x^55+409x^56+364x^57+315x^58+300x^59+241x^60+136x^61+87x^62+104x^63+50x^64+28x^65+30x^66+8x^67+7x^68+8x^70

The gray image is a linear code over GF(2) with n=224, k=12 and d=100.
This code was found by Heurico 1.16 in 0.64 seconds.