The generator matrix

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

generates a code of length 71 over Z4 who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+222x^60+542x^62+731x^64+788x^66+930x^68+898x^70+1035x^72+910x^74+728x^76+610x^78+385x^80+244x^82+120x^84+38x^86+7x^88+2x^90+1x^96

The gray image is a code over GF(2) with n=142, k=13 and d=60.
This code was found by Heurico 1.10 in 4.18 seconds.