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

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

Homogenous weight enumerator: w(x)=1x^0+301x^56+720x^58+1149x^60+16x^61+1378x^62+240x^63+2414x^64+1232x^65+3866x^66+2608x^67+4890x^68+2608x^69+3934x^70+1232x^71+2366x^72+240x^73+1596x^74+16x^75+985x^76+574x^78+275x^80+90x^82+31x^84+2x^86+3x^88+1x^116

The gray image is a code over GF(2) with n=272, k=15 and d=112.
This code was found by Heurico 1.16 in 68.8 seconds.