The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  0  1  1  2  1  1  0  2  1  1  1  0  2  1  1  0  1  2  0  0  1  1  1  1  2  2  1  1  2  2  0  1  1  0  2  1  1  0  0  1  2  4  1  1  1  4  1  2  1  1  2  2  2  1  2  1  1  1  1  1  1
 0  2  0  6  0  6  0  6  0  6  0  6  4  6  0  6  0  6  0  6  0  6  2  0  6  2  6  2  6  0  6  4  6  2  6  0  4  2  2  6  4  6  2  2  6  2  2  2  0  0  6  6  6  0  6  6  6  4  4  6  2  6  6  4  2  2  6  2  2  0  2  0  4  2  6  4  2  4  2  6  2  6  2  6  0  0  0  0
 0  0  4  0  0  0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  4  4  4  4  4  4  4  4  0  4  4  0  4  4  4  4  0  0  4  4  4  0  0  0  4  0  4  0  4  4  0  0  0  0  4  0  4  4  0  0  4  0  0  4  4  0  4  0  4  4  4  4  0  0  0  0  0  0  0
 0  0  0  4  0  0  0  0  0  0  0  0  0  0  4  0  4  0  0  4  0  0  0  4  0  0  4  4  0  4  0  4  4  0  4  0  4  4  0  0  0  0  4  4  4  4  4  4  4  4  4  0  4  0  4  4  4  4  0  4  4  4  4  0  0  0  0  4  0  0  4  4  0  0  4  0  4  0  0  0  4  4  0  0  0  0  0  0
 0  0  0  0  4  0  0  0  0  0  0  0  0  0  4  4  0  0  4  0  0  4  0  0  4  0  4  0  4  0  0  4  4  4  4  0  0  0  0  4  4  4  4  4  4  4  4  0  0  4  0  0  0  4  4  4  4  4  4  4  4  0  4  4  0  4  4  4  0  4  4  0  0  0  0  0  4  0  0  0  0  4  4  4  0  0  0  0
 0  0  0  0  0  4  0  0  0  0  0  0  0  4  0  4  4  4  4  0  4  4  4  0  4  0  0  4  4  0  0  4  4  0  0  0  0  4  4  4  4  4  4  4  0  0  0  0  4  4  4  4  4  0  4  0  4  4  4  4  0  0  0  4  4  0  0  0  0  0  4  0  0  4  4  4  0  0  4  0  0  0  4  4  4  4  0  0
 0  0  0  0  0  0  4  0  0  0  0  0  4  0  0  0  0  4  4  4  4  0  0  0  4  4  4  0  4  0  4  4  4  0  0  0  4  4  0  0  0  4  4  4  0  4  4  0  0  0  4  0  4  0  4  0  0  4  0  4  0  4  4  0  4  4  4  4  4  4  4  0  0  4  0  4  4  4  0  4  4  4  0  4  4  4  0  0
 0  0  0  0  0  0  0  4  0  0  0  0  0  4  0  0  4  0  4  0  4  4  4  4  0  4  4  0  4  0  4  0  4  4  0  0  4  4  0  4  0  4  0  4  4  0  4  0  0  0  0  0  4  4  0  4  4  0  0  0  4  0  0  4  4  0  4  0  0  0  4  0  4  4  4  0  4  0  0  4  4  4  0  4  0  0  0  0
 0  0  0  0  0  0  0  0  4  0  0  0  4  0  0  0  0  0  0  0  4  4  4  4  4  0  0  4  4  0  4  0  4  0  4  4  0  0  0  4  4  0  4  4  0  4  0  4  4  0  4  0  4  4  4  0  4  0  0  0  0  4  0  4  4  4  0  0  4  4  0  4  0  4  0  4  4  0  4  0  4  0  4  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  4  0  0  0  4  4  0  0  4  0  0  0  0  4  0  4  4  0  4  0  4  4  0  0  0  4  4  4  0  0  0  4  4  0  4  0  4  4  0  0  4  0  4  0  4  0  0  0  4  0  4  4  4  4  0  4  4  4  0  0  0  4  0  4  0  0  4  0  4  4  0  4  0  4  0  4  4  0  0
 0  0  0  0  0  0  0  0  0  0  4  0  4  0  0  0  0  0  0  0  0  0  0  0  0  4  4  4  4  4  0  4  0  0  0  4  0  4  4  4  4  0  4  4  0  0  4  0  4  0  4  4  4  4  0  4  4  4  4  0  0  4  4  0  4  0  4  4  0  4  4  4  4  0  4  0  0  4  0  4  0  4  4  4  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  4  0  4  4  4  4  0  0  4  4  0  0  4  0  0  0  4  4  0  4  0  4  4  0  4  4  0  0  4  0  4  4  0  4  4  0  0  4  4  4  0  4  0  0  0  0  0  0  4  0  0  4  0  0  4  0  0  4  4  0  0  4  0  4  4  4  0  4  0  0  4  4  0  0  0  0  0

generates a code of length 88 over Z8 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+54x^68+10x^70+270x^72+104x^74+668x^76+12x^77+484x^78+84x^79+1478x^80+292x^81+1614x^82+700x^83+2794x^84+1272x^85+2912x^86+1736x^87+3799x^88+1736x^89+2886x^90+1272x^91+2886x^92+700x^93+1628x^94+292x^95+1471x^96+84x^97+506x^98+12x^99+544x^100+86x^102+242x^104+10x^106+86x^108+34x^112+8x^116+1x^120

The gray image is a code over GF(2) with n=352, k=15 and d=136.
This code was found by Heurico 1.16 in 99.8 seconds.