The generator matrix

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

generates a code of length 78 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+166x^68+396x^70+439x^72+466x^74+498x^76+426x^78+433x^80+340x^82+330x^84+234x^86+169x^88+104x^90+70x^92+16x^94+6x^96+2x^98

The gray image is a code over GF(2) with n=156, k=12 and d=68.
This code was found by Heurico 1.10 in 1.02 seconds.