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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+80x^67+164x^68+198x^69+264x^70+320x^71+367x^72+388x^73+445x^74+426x^75+435x^76+436x^77+435x^78+444x^79+395x^80+482x^81+464x^82+396x^83+370x^84+354x^85+281x^86+248x^87+227x^88+148x^89+115x^90+122x^91+78x^92+36x^93+43x^94+12x^95+10x^96+6x^97+1x^102+1x^108

The gray image is a code over GF(2) with n=158, k=13 and d=67.
This code was found by Heurico 1.10 in 4.72 seconds.