The generator matrix

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

generates a code of length 44 over Z8 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+74x^34+230x^35+525x^36+1000x^37+1612x^38+2536x^39+3647x^40+4956x^41+6436x^42+7732x^43+8060x^44+7498x^45+6553x^46+5110x^47+3805x^48+2554x^49+1480x^50+860x^51+455x^52+246x^53+98x^54+42x^55+19x^56+2x^57+2x^58+2x^59+1x^78

The gray image is a code over GF(2) with n=176, k=16 and d=68.
This code was found by Heurico 1.16 in 82.8 seconds.