The generator matrix

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

generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+74x^30+156x^31+250x^32+402x^33+498x^34+598x^35+810x^36+944x^37+1080x^38+1188x^39+1292x^40+1472x^41+1438x^42+1352x^43+1220x^44+1006x^45+779x^46+612x^47+442x^48+300x^49+207x^50+122x^51+69x^52+34x^53+15x^54+4x^55+11x^56+2x^57+5x^58+1x^60

The gray image is a linear code over GF(2) with n=82, k=14 and d=30.
This code was found by Heurico 1.10 in 6 seconds.