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

generates a code of length 68 over Z8 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+14x^53+83x^54+84x^55+211x^56+180x^57+359x^58+346x^59+759x^60+558x^61+1512x^62+776x^63+2786x^64+988x^65+4174x^66+1104x^67+4782x^68+1110x^69+4220x^70+1038x^71+2841x^72+908x^73+1559x^74+570x^75+680x^76+258x^77+276x^78+148x^79+169x^80+68x^81+79x^82+28x^83+50x^84+12x^85+21x^86+2x^87+8x^88+2x^90+1x^92+3x^98

The gray image is a code over GF(2) with n=272, k=15 and d=106.
This code was found by Heurico 1.16 in 66.5 seconds.