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  1  1  1  1  1  1  1  1  X  0 X^2 X^2  1  1 X^2  1  X  1  1 X^2  X  X  1  X  1  1  1  1  1 X^2  1 X^2  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2  X X^2  X X^2+X X^2+X  X X^2  0  X  0  X  X  0 X^2  0 X^2+X X^2+X X^2 X^2 X^2  X  X  0  X X^2 X^2  0  0  X  0 X^2+X  X  X X^2+X X^2 X^2+X X^2 X^2+X  0  X  X  X
 0  0  X  0  0  0  X X^2+X  X  X  X  0  X  0 X^2 X^2 X^2 X^2  0 X^2+X  X  X X^2+X X^2  X X^2+X  0 X^2+X X^2+X  0 X^2+X  X X^2  X  X X^2  X X^2  X X^2+X  X  X  X  X  0 X^2  X  X  X  X X^2  X  X X^2+X  0  X
 0  0  0  X  0  X  X  X X^2  0  0 X^2  X X^2 X^2+X  X X^2 X^2+X  X  X X^2+X  X X^2 X^2+X  X  0  0  0  0 X^2+X X^2+X  X  0 X^2 X^2+X  0 X^2  0 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X X^2  0 X^2+X X^2+X X^2+X  X  0 X^2+X  0 X^2+X X^2
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  X X^2+X X^2  0  X X^2 X^2+X X^2 X^2+X X^2  0 X^2+X  0 X^2+X X^2  0 X^2+X X^2+X X^2+X X^2+X  X  X  X  0 X^2+X  X  0  X  0  0 X^2  X  X X^2 X^2 X^2 X^2+X  0 X^2 X^2+X X^2+X  0 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  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+121x^48+292x^50+56x^51+396x^52+176x^53+464x^54+280x^55+599x^56+288x^57+488x^58+168x^59+342x^60+48x^61+168x^62+8x^63+106x^64+52x^66+30x^68+8x^70+4x^72+1x^88

The gray image is a linear code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 1.05 seconds.