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  2  2  2  2  4  0  1  1  2  4  2  4  0  1  1  2  1  1  1  4  1  2  1  0  0  8  1  1  1  1  1  4
 0 12  0  0  0  0  0  0  0  0  8  4 12 12  8  0 12 12  4  4  8  4  0 12 12  4  4  4 12  8  8  4 12  8  4 12 12  4  4 12  4  4  4  0  8 12  8  8  0  0 12  8  8  0  8  8  8  4  8  0  4  8  0  0 12  4  0  8
 0  0 12  0  0  0  0  0  0  0 12  8  4 12  4  4  4 12  0  8 12 12  4  4 12  8  0 12  0  4 12  0  8  0  8 12  4  0 12 12  8  4  0  8  4 12  8  0  8  8  8  8  0 12  8  4  8  8  4  4 12  4  0 12  0  8 12  8
 0  0  0 12  0  0  8 12 12  4  4 12  8 12 12  0  8 12 12  8  0  8 12 12 12  0  4  0  4  4  8  0 12  0  8  8 12  4  0  8 12  8  0  4  0 12  4  4  8  8  4 12 12  0  4  8  4  0  0  8  4  8  8  4 12  0  0 12
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  8  0 12  4  4 12  4  0  4 12  0 12 12 12  8 12  4  0  8  0 12  8  0  8  8  0  4  4  8  0  4  0 12  8  0  8  8 12  0  4  8  4  4  4  8  0  4  4  8  0  0  8  4  0
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  4  4  0  8  4  4  0  4 12 12 12  8  8 12  4  0 12  4  4  8  0  8  8  0  8  4 12  0  0  8 12  8  8  8  4  4  8  0  8  4 12 12  8  4  8  4 12  8  4  8  4 12 12  8

generates a code of length 68 over Z16 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+65x^58+130x^59+201x^60+268x^61+307x^62+548x^63+815x^64+1190x^65+1604x^66+1964x^67+2232x^68+2092x^69+1675x^70+1166x^71+735x^72+408x^73+288x^74+216x^75+136x^76+104x^77+76x^78+70x^79+35x^80+34x^81+15x^82+2x^83+2x^84+2x^86+2x^88+1x^100

The gray image is a code over GF(2) with n=544, k=14 and d=232.
This code was found by Heurico 1.16 in 8.03 seconds.