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

generates a code of length 86 over Z8 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+66x^84+128x^86+49x^88+6x^92+5x^96+1x^120

The gray image is a code over GF(2) with n=344, k=8 and d=168.
This code was found by Heurico 1.16 in 12.3 seconds.