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

generates a code of length 67 over Z16 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+85x^58+8x^59+260x^60+16x^61+329x^62+112x^63+476x^64+592x^65+1464x^66+1608x^67+1473x^68+592x^69+391x^70+128x^71+288x^72+16x^73+166x^74+109x^76+52x^78+14x^80+9x^82+2x^84+1x^104

The gray image is a code over GF(2) with n=536, k=13 and d=232.
This code was found by Heurico 1.16 in 2.01 seconds.