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 1 1 1 1 1 1 1 1 1 X X X 1 X X 1 1 1 X 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X 0 X X 0 X 0 X X 0 X X X 0 0 0 X X
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 X 0 0 X 0 0 X X 0 X 0 0 0 X X X X X 0 X 0 X X
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X X 0 X 0 0 X X 0 0 0 0 X X X X X 0 X 0 0 X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X 0 0 0 X X 0 0 0 X X X 0 X 0 X X 0 0 X
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X 0 X 0 0 X X 0 0 0 0 X 0 X 0 0 X 0 X X 0 0 X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 X 0 0 X 0 X 0 X 0 0 X X X X 0 X X 0 0 0 X X X
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 0 X X 0 X 0 X 0 0 X X X X X 0 X X 0 0 0 X 0 X
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X 0 X X X X X X X X 0 X 0 0 0 X X 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 X X X 0 0 X 0 0 X 0 0 X 0 X X 0 X X X 0
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 0 0 0 0 0 X X 0 0 X 0 0 X X X X 0 X X X
generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.
Homogenous weight enumerator: w(x)=1x^0+46x^38+115x^40+161x^42+167x^44+32x^45+168x^46+192x^47+176x^48+480x^49+184x^50+640x^51+202x^52+480x^53+187x^54+192x^55+187x^56+32x^57+164x^58+115x^60+94x^62+49x^64+18x^66+12x^68+1x^70+1x^90
The gray image is a linear code over GF(2) with n=102, k=12 and d=38.
This code was found by Heurico 1.16 in 2.75 seconds.