The generator matrix

 1  0  0  0  0  1  1  1  1  1  1  1  X  X  X  0  0  X  0  X  X  X  0  1  1  0  X  1  1  1  1  1  0  1  1  1  1  X  1  1  1  0  1  0  1  1  X  X  0  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  0  1  0  0  1  1  0  1  1  1  1  1  1  1  0  0  1  0  1  X  0  X  X  X  0  1 X+1  X  X  0 X+1  0  X  0  0  X  X  X X+1  1 X+1  X  1  X  1  0  0  1 X+1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  1  0  0  1  0  1  1  0  1  0  1  0  0  1  X X+1  1  1  1  1 X+1  X  1  0  1  0  1  X  0  1  X X+1 X+1  X  1  1  0  1  1  1  0 X+1  X X+1 X+1  1  X  X X+1  1 X+1  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  1  0  1  1  1  0  0  0  1  1  0  0 X+1 X+1  0 X+1 X+1 X+1 X+1  X X+1 X+1  1 X+1  0  X  1  1 X+1  1  0  1  0  1  X  1  0  0  1  0  X X+1  X X+1  1  1  X  1 X+1  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  0  1  1  X  1  1  1  X X+1 X+1  1  X X+1  X  X  X X+1  1  1  0  0  X X+1  X X+1  X X+1 X+1  X  1  1 X+1  0  0  0 X+1 X+1 X+1  0 X+1  0  X  1  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  0  0  X  0  X  X  0  X  0  X  X  X  0  X  0  X  X  X  0  X  X  0  X  X  0  0  X  X  X  X  0  X  X  0  0  0  X  X  0  0  0  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  0  0  0  X  X  X  0  0  X  X  0  0  X  X  0  0  X  X  X  X  X  X  X  0  0  X  0  X  0  0  0  0  X  0  0  0  X  X  0  0  X  X  X  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  X  0  0  X  0  X  0  X  0  X  0  X  0  X  X  0  0  0  X  0  0  X  0  X  X  X  0  X  0  X  0  0  0  X  0  X  0  0  X  X  X  0  X  0  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  X  0  X  0  0  X  X  X  0  0  X  X  0  X  0  X  X  0  0  X  0  X  X  X  0  0  X  0  X  0  X  0  X  0  0  0  X  0  0  X  0  0  0  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  0  X  X  X  0  0  X  0  X  0  0  X  0  0  0  0  X  X  X  X  0  0  X  0  0  X  X  X  X  X  X  0  X  X  X  0  0  X  0  X  X  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+57x^40+165x^42+296x^44+559x^46+738x^48+991x^50+1244x^52+1335x^54+58x^55+1057x^56+202x^57+715x^58+416x^59+541x^60+762x^61+261x^62+1324x^63+127x^64+1840x^65+65x^66+2294x^67+30x^68+2570x^69+25x^70+2278x^71+55x^72+1876x^73+145x^74+1388x^75+350x^76+750x^77+523x^78+368x^79+736x^80+176x^81+992x^82+62x^83+1218x^84+14x^85+1278x^86+4x^87+1063x^88+2x^89+825x^90+521x^92+247x^94+130x^96+54x^98+24x^100+12x^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 98.6 seconds.