The generator matrix

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

generates a code of length 79 over Z8 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+388x^72+228x^73+840x^74+328x^75+1098x^76+380x^77+1028x^78+316x^79+859x^80+280x^81+698x^82+292x^83+586x^84+112x^85+354x^86+68x^87+172x^88+20x^89+86x^90+20x^91+28x^92+4x^93+2x^94+4x^96

The gray image is a code over GF(2) with n=316, k=13 and d=144.
This code was found by Heurico 1.11 in 9.7 seconds.