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

generates a code of length 86 over Z8 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+125x^56+308x^60+465x^64+610x^68+4x^70+749x^72+62x^74+827x^76+380x^78+1199x^80+1954x^82+5926x^84+7488x^86+6034x^88+1954x^90+1157x^92+380x^94+811x^96+62x^98+731x^100+4x^102+678x^104+478x^108+214x^112+129x^116+26x^120+10x^124+2x^128

The gray image is a code over GF(2) with n=344, k=15 and d=112.
This code was found by Heurico 1.16 in 99.2 seconds.