The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+54x^43+159x^44+284x^45+405x^46+466x^47+570x^48+760x^49+793x^50+860x^51+1013x^52+1096x^53+1117x^54+1166x^55+1143x^56+1036x^57+1107x^58+994x^59+828x^60+730x^61+528x^62+390x^63+349x^64+234x^65+136x^66+100x^67+28x^68+18x^69+10x^70+2x^71+4x^72+2x^73+1x^96

The gray image is a linear code over GF(2) with n=110, k=14 and d=43.
This code was found by an older version of Heurico in 0 seconds.