The generator matrix

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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+30x^40+147x^42+232x^44+387x^46+681x^48+885x^50+1121x^52+1207x^54+1154x^56+925x^58+594x^60+429x^62+354x^64+329x^66+585x^68+947x^70+1632x^72+2200x^74+2498x^76+2654x^78+2098x^80+1606x^82+1088x^84+530x^86+310x^88+303x^90+446x^92+684x^94+946x^96+1027x^98+1192x^100+1213x^102+901x^104+633x^106+393x^108+229x^110+116x^112+41x^114+10x^116+7x^118+1x^120+1x^124+1x^126

The gray image is a linear code over GF(2) with n=154, k=15 and d=40.
This code was found by Heurico 1.16 in 98.6 seconds.