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

generates a code of length 68 over Z8 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+60x^56+76x^57+196x^58+272x^59+324x^60+490x^61+566x^62+752x^63+924x^64+1030x^65+1297x^66+1472x^67+1470x^68+1478x^69+1337x^70+1142x^71+950x^72+724x^73+507x^74+402x^75+281x^76+182x^77+143x^78+106x^79+74x^80+50x^81+43x^82+14x^83+9x^84+2x^85+6x^86+3x^88+1x^98

The gray image is a code over GF(2) with n=272, k=14 and d=112.
This code was found by Heurico 1.16 in 17.4 seconds.