The generator matrix

 1  0  0  0  0  0  1  1  1  1  1  1  1  0  1  0  1  1  1  0  2  1  1  1  1  1  2  0  0  1  2  1  1  1  1  2  1  2  0  1  0  0  1  1  1  2  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  1  1  1  1  1
 0  1  0  0  0  0  1  0  0  1  0  3  2  2  2  1  2  3  2  1  1  3  1  3  3  1  1  1  2  2  1  2  0  1  2  1  2  1  2  1  1  0  3  1  1  1  3  0  2  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
 0  0  1  0  0  0  1  0  1  1  0  0  3  1  0  2  3  2  1  2  0  3  2  2  2  1  2  2  1  3  3  2  3  0  1  0  0  0  2  1  1  0  1  0  1  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  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  3  1  2  3  2  0  2  0  0  3  0  1  3  3  0  2  3  2  0  2  2  1  3  0  1  2  0  1  1  1  0  0  0  0  0  1  0  0  0  0  2  0  0  0  2  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  1  1  0  0  1  0  1  1  2  2  1  3  0  2  0  0  0  1  1  0  1  1  3  2  0  0  3  2  2  3  0  3  0  3  0  2  1  1  0  0  0  1  0  0  0  0  2  2  0  0  2  2  0  0  0  2  2  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  2  2  3  1  1  1  0  2  2  3  2  0  3  2  1  2  3  0  3  0  0  1  1  1  3  1  1  1  0  2  1  0  0  3  1  1  0  0  0  0  0  0  0  0  0  0  0  0  2  2  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  2  0  0  0  2  2  2  0  0  2  2  0  2  0  2  2  2  0  2  2  0  2  2  2  0  0  0  0  0  2  2  0  0  2  0  0  0  0  0  2  2  0  0  2  0  2  2  0  0  0  2  0  0  0  2  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  2  0  2  2  0  0  2  2  2  2  0  2  0  0  2  2  0  2  2  2  2  0  0  0  2  2  0  2  0  0  0  2  0  0  2  0  2  0  0  2  0  2  2  2  2  0  0  0  0  0  0  0  0  2  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  2  2  0  2  2  0  2  2  2  0  0  2  0  0  0  2  2  2  2  2  2  0  0  2  0  0  0  2  2  2  0  0  2  2  0  2  0  0  2  2  2  0  2  0  0  0  2  0  0  0  0  2  2  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 86 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+21x^40+28x^42+60x^44+81x^46+212x^48+297x^50+503x^52+673x^54+769x^56+915x^58+1007x^60+982x^62+787x^64+673x^66+469x^68+289x^70+22x^71+216x^72+58x^73+125x^74+228x^75+49x^76+482x^77+31x^78+992x^79+2x^80+1654x^81+2x^82+2116x^83+2612x^85+2602x^87+4x^88+2218x^89+2x^90+1672x^91+12x^92+958x^93+26x^94+472x^95+46x^96+198x^97+108x^98+80x^99+181x^100+12x^101+312x^102+8x^103+494x^104+673x^106+824x^108+952x^110+1004x^112+916x^114+786x^116+662x^118+486x^120+285x^122+176x^124+123x^126+78x^128+30x^130+5x^132+4x^134+2x^138+1x^142

The gray image is a code over GF(2) with n=172, k=15 and d=40.
This code was found by Heurico 1.16 in 99.3 seconds.