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

generates a code of length 86 over Z8 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+125x^68+344x^72+8x^74+525x^76+118x^78+774x^80+482x^82+3388x^84+4924x^86+3310x^88+492x^90+842x^92+110x^94+469x^96+10x^98+289x^100+118x^104+44x^108+8x^112+2x^116+1x^140

The gray image is a code over GF(2) with n=344, k=14 and d=136.
This code was found by Heurico 1.16 in 32.2 seconds.