The generator matrix

 1  0  0  1  1  1  6  1  0  1  6  1  1  2  1  2  1  2  0  1  1  1  1  1  0  4  0  1  0  1  1  1  4  2  1  1  6  1  6  6  1  4  1  1  0  6  1  6  2  1  1  1  1  4  1  1  1  1  1  4  0  1  1  1  1  1  1  6  4  1  1  6  6  1  1  4  4  1
 0  1  0  0  1  1  1  6  1  6  1  1  5  2  5  2  2  1  1  6  3  2  6  7  1  6  1  0  1  7  4  0  4  1  1  7  2  7  6  1  6  1  6  1  1  0  5  1  0  7  3  4  1  1  6  3  5  2  2  4  1  4  5  0  1  5  3  1  1  6  5  1  2  4  6  1  2  3
 0  0  1  1  1  0  1  5  0  4  7  3  2  1  0  1  1  6  3  2  3  5  4  7  7  1  2  0  5  2  5  4  1  4  6  0  1  3  1  3  3  4  6  5  3  1  7  1  1  3  4  4  0  2  5  5  2  1  4  1  4  5  6  3  3  6  6  2  3  6  5  7  1  5  5  2  1  7
 0  0  0  2  0  0  4  4  2  6  6  2  2  6  2  0  6  6  6  4  0  0  6  6  4  2  0  6  6  4  0  6  6  2  0  2  2  0  6  4  2  0  6  4  2  4  6  4  0  0  4  2  0  2  4  2  6  2  4  0  0  2  2  0  2  6  4  4  0  6  6  6  0  2  2  4  2  2
 0  0  0  0  2  0  2  6  6  2  4  0  6  2  6  2  6  0  6  6  0  4  4  6  0  4  2  4  2  4  2  6  6  4  2  4  6  0  4  0  0  4  6  6  0  2  6  2  4  6  2  0  6  4  4  6  2  0  4  4  4  6  4  2  4  4  6  6  2  4  6  2  0  6  4  0  2  2
 0  0  0  0  0  2  4  0  0  0  4  4  6  0  4  4  4  4  0  4  4  4  4  4  4  0  4  4  0  4  4  0  0  0  6  6  2  2  2  6  2  2  6  2  6  2  2  6  6  6  4  6  2  2  2  6  2  6  0  2  6  4  6  2  2  0  6  2  2  4  6  4  0  2  2  4  4  0

generates a code of length 78 over Z8 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+253x^68+264x^69+948x^70+792x^71+1492x^72+1544x^73+2200x^74+2052x^75+2881x^76+2476x^77+3116x^78+2652x^79+2682x^80+1976x^81+2368x^82+1532x^83+1366x^84+776x^85+666x^86+204x^87+235x^88+64x^89+124x^90+66x^92+4x^93+18x^94+14x^96+2x^100

The gray image is a code over GF(2) with n=312, k=15 and d=136.
This code was found by Heurico 1.16 in 64.4 seconds.