The generator matrix

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

generates a code of length 78 over Z8 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+202x^72+310x^73+453x^74+406x^75+421x^76+332x^77+408x^78+256x^79+267x^80+154x^81+222x^82+136x^83+174x^84+96x^85+76x^86+64x^87+62x^88+20x^89+5x^90+18x^91+9x^92+4x^94

The gray image is a code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.16 in 0.753 seconds.