The generator matrix

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

generates a code of length 78 over Z8 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+8x^34+16x^35+8x^36+24x^37+19x^38+44x^39+34x^40+122x^41+66x^42+220x^43+112x^44+324x^45+161x^46+562x^47+223x^48+752x^49+241x^50+916x^51+238x^52+1014x^53+261x^54+804x^55+246x^56+592x^57+186x^58+414x^59+138x^60+198x^61+71x^62+90x^63+34x^64+80x^65+67x^66+68x^67+90x^68+226x^69+212x^70+606x^71+494x^72+1764x^73+1882x^74+4268x^75+4514x^76+7366x^77+5958x^78+7400x^79+4496x^80+4210x^81+1884x^82+1810x^83+530x^84+648x^85+218x^86+168x^87+102x^88+96x^89+46x^90+54x^91+43x^92+78x^93+61x^94+204x^95+124x^96+402x^97+179x^98+652x^99+226x^100+838x^101+265x^102+968x^103+279x^104+968x^105+226x^106+652x^107+212x^108+510x^109+178x^110+412x^111+110x^112+208x^113+58x^114+126x^115+32x^116+54x^117+35x^118+22x^119+1x^120+6x^121+4x^122+4x^123+1x^124+1x^126+1x^130

The gray image is a code over GF(2) with n=312, k=16 and d=68.
This code was found by Heurico 1.16 in 97.4 seconds.