The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  2  1  1  1  1  2  2  0  1  1  2  1  0  0  1  1  2  1  1  1  2  1  0  0  2  0  1  1  0  2  1  1  1  1  0  2  2  1  1  1  2  1  2  2  2  2  1  0  0  1  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  2  2  1  0  1  1  1  1
 0  1  0  1  0  1  1  0  0  1  3  1  2  1  0  2  3  1  1  1  0  3  0  1  0  1  0  3  1  2  2  0  3  1  0  1  1  1  1  2  2  1  1  3  3  3  3  1  0  0  1  2  0  1  0  1  1  0  2  2  1  1  1  3  1  1  2  2  3  1  2  2  3  2  2  2  3  1  1  1  2  2  2  2  1  0
 0  0  1  1  1  0  1  0  1  1  0  2  1  3  3  2  0  3  2  3  1  3  2  3  3  2  1  0  0  1  1  0  1  1  1  3  1  2  2  0  1  2  3  2  2  1  3  1  1  1  1  3  2  3  1  2  0  1  1  0  1  0  3  3  1  0  2  1  0  0  1  2  3  1  1  2  3  2  0  3  3  1  0  2  1  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  0  0  2  0  0  2  2  2  0  2  0  0  0  0  2  2  2  0  2  2  0  2  0  2  2  0  0  0  2  2  0  0  0  2  0  2  2  0  0  0  0  2  2  2  0  0  0  0  0  2  2  2  0  0  2  0  2  0  2  2  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  0  0  0  2  2  0  0  2  0  2  2  0  2  0  2  0  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  2  0  0  0  2  2  0  0  0  2  0  2  0  2  2  2  0  0  2  0  0  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  0  0  2  0  2  0  0  2  2  0  0  0  2  2  0  0  0  0  0  2  2  0  0  0  2  2  2  0  2  2  0  2  0  2  0  0  2  2  2  0  2  2  0  2  2  2  0  0  2  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  0  0  2  0  0  2  0  2  2  2  0  2  2  2  0  2  2  2  2  0  2  2  2  0  0  2  2  2  0  0  2  0  2  2  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  0  2  0  0  2  0  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  0  2  2  2  0  2  2  0  2  0  0  2  0  0  0  2  0  0  2  0  2  2  0  2  0  2  0  2  0  2  2  2  0  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0  0  2  0  0  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  2  0  0  0  2  2  0  0  2  2  2  0  0  2  0  0  0  2  0  0  2  2  2  2  0  0  0  2  0  2  0  2  2  2  2  0  0  0  2  0  0  2  0  2  2  0  2  0  2  2  0  2  0  0  0  2  0  2  2  2  0  0  2  0  2  0  0  0  2  2  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  0  0  2  0  2  0  0  0  2  0  2  0  2  2  0  0  0  2  2  0  2  2  2  2  0  0  0  2  2  0  0  0  2  0  0  0  2  2  0  2  0  0

generates a code of length 86 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+71x^72+34x^73+142x^74+132x^75+222x^76+214x^77+303x^78+344x^79+324x^80+408x^81+388x^82+466x^83+412x^84+482x^85+407x^86+508x^87+488x^88+442x^89+359x^90+336x^91+276x^92+290x^93+256x^94+216x^95+187x^96+156x^97+132x^98+42x^99+44x^100+22x^101+35x^102+4x^103+17x^104+17x^106+6x^108+7x^110+2x^114

The gray image is a code over GF(2) with n=172, k=13 and d=72.
This code was found by Heurico 1.16 in 15.7 seconds.