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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+27x^40+28x^41+85x^42+110x^43+206x^44+202x^45+282x^46+362x^47+320x^48+442x^49+528x^50+572x^51+619x^52+656x^53+575x^54+654x^55+603x^56+636x^57+603x^58+608x^59+667x^60+670x^61+808x^62+860x^63+951x^64+1108x^65+1188x^66+1262x^67+1331x^68+1260x^69+1293x^70+1158x^71+1055x^72+902x^73+812x^74+664x^75+638x^76+616x^77+540x^78+534x^79+577x^80+664x^81+606x^82+684x^83+597x^84+600x^85+519x^86+496x^87+413x^88+314x^89+238x^90+190x^91+153x^92+76x^93+102x^94+32x^95+29x^96+18x^97+12x^98+6x^99+5x^100+1x^102

The gray image is a linear code over GF(2) with n=136, k=15 and d=40.
This code was found by Heurico 1.16 in 99.3 seconds.