The generator matrix

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

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+19x^40+42x^41+109x^42+110x^43+176x^44+212x^45+255x^46+330x^47+406x^48+426x^49+486x^50+624x^51+553x^52+638x^53+617x^54+576x^55+624x^56+560x^57+551x^58+512x^59+590x^60+606x^61+567x^62+692x^63+875x^64+972x^65+1000x^66+1242x^67+1349x^68+1264x^69+1263x^70+1252x^71+1179x^72+984x^73+813x^74+744x^75+667x^76+570x^77+506x^78+500x^79+529x^80+572x^81+632x^82+604x^83+571x^84+630x^85+562x^86+600x^87+532x^88+478x^89+399x^90+286x^91+285x^92+184x^93+144x^94+114x^95+71x^96+46x^97+26x^98+6x^99+17x^100+8x^101+6x^102+4x^104

The gray image is a linear code over GF(2) with n=138, k=15 and d=40.
This code was found by Heurico 1.16 in 99.2 seconds.