The generator matrix

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

generates a code of length 87 over Z4 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+59x^70+303x^72+831x^74+1341x^76+1832x^78+2336x^80+2717x^82+3194x^84+3636x^86+3705x^88+3483x^90+2916x^92+2379x^94+1665x^96+1163x^98+612x^100+346x^102+166x^104+54x^106+16x^108+10x^110+1x^118+1x^124+1x^126

The gray image is a code over GF(2) with n=174, k=15 and d=70.
This code was found by Heurico 1.10 in 76.2 seconds.