The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+82x^72+124x^73+219x^74+370x^75+455x^76+552x^77+585x^78+650x^79+690x^80+664x^81+810x^82+808x^83+832x^84+896x^85+910x^86+930x^87+852x^88+906x^89+801x^90+738x^91+681x^92+610x^93+497x^94+430x^95+371x^96+284x^97+226x^98+148x^99+111x^100+52x^101+46x^102+22x^103+20x^104+6x^105+2x^109+2x^110+1x^132

The gray image is a code over GF(2) with n=172, k=14 and d=72.
This code was found by Heurico 1.10 in 19.7 seconds.