The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+116x^45+412x^46+1078x^47+1581x^48+2962x^49+4050x^50+5752x^51+7636x^52+9904x^53+11227x^54+13788x^55+13399x^56+13798x^57+11677x^58+10594x^59+7731x^60+5926x^61+3847x^62+2516x^63+1415x^64+868x^65+381x^66+182x^67+107x^68+86x^69+22x^70+10x^71+4x^73+2x^76

The gray image is a linear code over GF(2) with n=224, k=17 and d=90.
This code was found by Heurico 1.13 in 165 seconds.