The generator matrix

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

generates a code of length 72 over Z8 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+8x^34+8x^35+21x^36+26x^37+35x^38+84x^39+107x^40+200x^41+204x^42+344x^43+386x^44+474x^45+629x^46+616x^47+685x^48+638x^49+692x^50+600x^51+539x^52+488x^53+351x^54+282x^55+255x^56+174x^57+110x^58+98x^59+60x^60+80x^61+99x^62+152x^63+314x^64+490x^65+906x^66+1844x^67+2600x^68+3532x^69+5102x^70+6400x^71+6514x^72+5750x^73+5142x^74+4130x^75+2604x^76+1592x^77+984x^78+516x^79+232x^80+134x^81+86x^82+72x^83+48x^84+110x^85+133x^86+158x^87+196x^88+332x^89+397x^90+476x^91+584x^92+604x^93+712x^94+618x^95+745x^96+582x^97+512x^98+506x^99+372x^100+326x^101+246x^102+202x^103+86x^104+74x^105+29x^106+42x^107+32x^108+8x^109+4x^110+4x^111+1x^112+2x^113+2x^114+2x^116+1x^118

The gray image is a code over GF(2) with n=288, k=16 and d=68.
This code was found by Heurico 1.16 in 99.8 seconds.