The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+82x^68+446x^69+776x^70+1092x^71+1446x^72+1874x^73+1918x^74+2460x^75+2479x^76+2734x^77+2611x^78+2508x^79+2533x^80+2498x^81+1849x^82+1804x^83+1203x^84+878x^85+634x^86+392x^87+242x^88+156x^89+75x^90+48x^91+14x^92+2x^93+9x^94+4x^97

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 40.6 seconds.