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

generates a code of length 78 over Z8 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+120x^56+343x^60+544x^64+863x^68+140x^70+1462x^72+980x^74+2828x^76+18232x^78+2789x^80+1000x^82+1485x^84+124x^86+847x^88+4x^90+572x^92+286x^96+111x^100+31x^104+5x^108+1x^132

The gray image is a code over GF(2) with n=312, k=15 and d=112.
This code was found by Heurico 1.16 in 99 seconds.