The generator matrix

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

generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+38x^39+138x^40+250x^41+332x^42+418x^43+633x^44+688x^45+760x^46+938x^47+1016x^48+1144x^49+1214x^50+1212x^51+1150x^52+1206x^53+1109x^54+940x^55+857x^56+674x^57+533x^58+416x^59+258x^60+176x^61+143x^62+68x^63+40x^64+20x^65+5x^66+2x^67+2x^68+2x^69+1x^84

The gray image is a linear code over GF(2) with n=102, k=14 and d=39.
This code was found by an older version of Heurico in 0 seconds.