The generator matrix

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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+51x^68+70x^69+119x^70+176x^71+223x^72+264x^73+261x^74+246x^75+200x^76+226x^77+225x^78+224x^79+232x^80+182x^81+171x^82+198x^83+161x^84+188x^85+144x^86+112x^87+127x^88+70x^89+60x^90+50x^91+48x^92+20x^93+8x^94+16x^95+13x^96+4x^97+4x^98+2x^99

The gray image is a code over GF(2) with n=158, k=12 and d=68.
This code was found by Heurico 1.10 in 1.02 seconds.