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

generates a code of length 76 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+5x^40+8x^41+41x^42+66x^43+110x^44+124x^45+148x^46+178x^47+282x^48+342x^49+399x^50+430x^51+505x^52+572x^53+586x^54+658x^55+590x^56+546x^57+476x^58+462x^59+356x^60+328x^61+296x^62+270x^63+243x^64+258x^65+265x^66+234x^67+459x^68+514x^69+624x^70+830x^71+995x^72+1108x^73+1145x^74+1294x^75+1254x^76+1280x^77+1290x^78+1028x^79+922x^80+792x^81+662x^82+602x^83+400x^84+276x^85+281x^86+220x^87+212x^88+228x^89+310x^90+324x^91+423x^92+450x^93+529x^94+574x^95+533x^96+650x^97+570x^98+578x^99+476x^100+478x^101+380x^102+320x^103+309x^104+194x^105+158x^106+106x^107+81x^108+38x^109+23x^110+18x^111+35x^112+2x^113+6x^114+4x^117+3x^118+1x^120

The gray image is a linear code over GF(2) with n=152, k=15 and d=40.
This code was found by Heurico 1.16 in 98.6 seconds.