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

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+52x^40+8x^41+72x^42+46x^43+180x^44+90x^45+299x^46+188x^47+401x^48+360x^49+470x^50+420x^51+550x^52+622x^53+608x^54+684x^55+513x^56+532x^57+376x^58+478x^59+249x^60+330x^61+183x^62+202x^63+124x^64+210x^65+156x^66+204x^67+266x^68+360x^69+516x^70+706x^71+769x^72+940x^73+1056x^74+1182x^75+1269x^76+1286x^77+1360x^78+1162x^79+1178x^80+926x^81+794x^82+672x^83+480x^84+404x^85+214x^86+246x^87+155x^88+160x^89+147x^90+200x^91+159x^92+318x^93+258x^94+476x^95+418x^96+590x^97+515x^98+624x^99+567x^100+626x^101+555x^102+468x^103+492x^104+336x^105+389x^106+210x^107+277x^108+76x^109+180x^110+12x^111+67x^112+18x^113+41x^114+12x^115+19x^116+3x^118+5x^120+1x^128

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 99.6 seconds.