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

generates a code of length 68 over Z8 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+64x^50+163x^52+256x^54+363x^56+437x^58+502x^60+583x^62+256x^63+653x^64+1280x^65+672x^66+2560x^67+17056x^68+2560x^69+749x^70+1280x^71+721x^72+256x^73+620x^74+568x^76+423x^78+305x^80+212x^82+105x^84+67x^86+36x^88+11x^90+6x^92+1x^94+1x^96+1x^126

The gray image is a code over GF(2) with n=272, k=15 and d=100.
This code was found by Heurico 1.16 in 85.1 seconds.