The generator matrix

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

generates a code of length 85 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+42x^72+98x^73+188x^74+218x^75+282x^76+352x^77+317x^78+368x^79+445x^80+384x^81+368x^82+446x^83+464x^84+480x^85+442x^86+392x^87+389x^88+388x^89+349x^90+366x^91+278x^92+240x^93+206x^94+176x^95+160x^96+72x^97+102x^98+74x^99+46x^100+32x^101+10x^102+8x^103+3x^104+2x^105+1x^106+2x^108+1x^110

The gray image is a code over GF(2) with n=170, k=13 and d=72.
This code was found by Heurico 1.10 in 5.07 seconds.