The generator matrix

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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+15x^40+67x^42+133x^44+228x^46+460x^48+688x^50+883x^52+1039x^54+1127x^56+1072x^58+899x^60+678x^62+449x^64+276x^66+171x^68+297x^70+550x^72+933x^74+1562x^76+2242x^78+2592x^80+2630x^82+2254x^84+1544x^86+984x^88+542x^90+266x^92+172x^94+259x^96+427x^98+684x^100+904x^102+1099x^104+1181x^106+1035x^108+891x^110+624x^112+441x^114+267x^116+96x^118+61x^120+29x^122+5x^124+5x^126+3x^128+2x^130+1x^132

The gray image is a linear code over GF(2) with n=162, k=15 and d=40.
This code was found by Heurico 1.16 in 99.5 seconds.