The generator matrix

X X 1 1 1 0 1 X 1 1 0 0 0 1 1 0 0 1 1 X 0 0 0 1 1 X 1 1 X 1 X X 1 1 X 1 1 0 X 0 0 1 X 1 0 X X 1 1 1 X 1 0 1 1 1
X 1 X 1 0 1 X+1 X 0 X+1 1 0 1 1 X X 1 X 0 0 0 X X 1 X+1 1 X X+1 1 1 1 X X+1 X X 0 0 1 1 0 X X+1 1 0 0 X 0 0 X+1 X 0 X 0 1 X 0
1 0 X X+1 X X 1 1 1 0 1 X X+1 X X+1 X 0 X 1 1 1 X X X+1 X+1 X+1 X+1 X X+1 0 X X X+1 X+1 1 0 X 0 1 1 X 1 X X+1 1 X 1 0 X 0 1 0 0 1 X+1 0
0 0 0 X 1 1 X+1 X+1 X 1 1 0 0 X X+1 1 X+1 X+1 0 X+1 0 X 1 X+1 X X 1 X+1 X+1 X+1 1 1 1 0 0 X 1 X 0 0 1 0 0 X+1 1 0 1 0 X 1 X+1 X+1 X 1 1 0
0 0 0 0 0 0 0 0 X X X 0 0 0 0 X X X X 0 0 0 0 X 0 0 0 X 0 X+1 1 1 X+1 1 1 X+1 X+1 1 X+1 1 1 X+1 X+1 X+1 1 1 X+1 X+1 X+1 X 1 1 1 X+1 0 1
0 0 0 0 0 0 X X X+1 X+1 1 1 1 X+1 X+1 1 0 X 1 0 X 1 1 0 0 1 X+1 1 X+1 1 X+1 0 X+1 0 1 X+1 X+1 X+1 0 1 0 X+1 X+1 X X X+1 0 X+1 X 0 1 0 X 1 0 X+1
0 0 0 0 0 0 0 0 X X X X X X 0 0 X X 0 X X 0 X X X 0 X 0 0 X 0 X 0 X 0 X X X X X 0 X X 0 X 0 0 0 0 0 0 0 X X X 0

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+44x^45+119x^46+240x^47+308x^48+336x^49+358x^50+436x^51+485x^52+478x^53+492x^54+498x^55+530x^56+508x^57+562x^58+524x^59+480x^60+484x^61+405x^62+280x^63+201x^64+180x^65+104x^66+64x^67+42x^68+18x^69+8x^70+6x^71+1x^100

The gray image is a linear code over GF(2) with n=112, k=13 and d=45.
This code was found by an older version of Heurico in 0 seconds.