The generator matrix

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

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+26x^40+65x^42+131x^44+285x^46+421x^48+682x^50+904x^52+989x^54+1145x^56+1065x^58+873x^60+679x^62+440x^64+256x^66+126x^68+4x^69+71x^70+100x^71+21x^72+246x^73+4x^74+486x^75+6x^76+982x^77+1554x^79+2x^80+2126x^81+2726x^83+2618x^85+2176x^87+1610x^89+906x^91+2x^92+514x^93+12x^94+218x^95+20x^96+82x^97+48x^98+26x^99+140x^100+10x^101+276x^102+437x^104+691x^106+884x^108+1028x^110+1125x^112+1036x^114+905x^116+665x^118+415x^120+256x^122+140x^124+74x^126+27x^128+8x^130+1x^132+1x^134+1x^138

The gray image is a linear code over GF(2) with n=168, k=15 and d=40.
This code was found by Heurico 1.16 in 99.8 seconds.