The generator matrix

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

generates a code of length 86 over Z4 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+48x^70+144x^71+279x^72+366x^73+443x^74+640x^75+732x^76+870x^77+1117x^78+1166x^79+1343x^80+1530x^81+1562x^82+1584x^83+1751x^84+1842x^85+1757x^86+1828x^87+1838x^88+1824x^89+1703x^90+1508x^91+1282x^92+1148x^93+1040x^94+874x^95+716x^96+562x^97+418x^98+244x^99+205x^100+154x^101+90x^102+68x^103+39x^104+22x^105+10x^106+8x^107+6x^108+2x^109+3x^110+1x^134

The gray image is a code over GF(2) with n=172, k=15 and d=70.
This code was found by Heurico 1.10 in 157 seconds.