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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+66x^61+119x^62+108x^63+101x^64+200x^65+420x^66+698x^67+814x^68+656x^69+404x^70+162x^71+62x^72+60x^73+82x^74+46x^75+10x^76+30x^77+29x^78+10x^79+3x^80+12x^81+2x^82+1x^112

The gray image is a code over GF(2) with n=544, k=12 and d=244.
This code was found by Heurico 1.16 in 57.4 seconds.