The generator matrix

 1  0  1  1  1 14  1  1  6  1  4  1  1  1  6  1  1  0  6  1  1  1  4  1  1  1  1  1  1 12 10  1  1  1  2  1  2  0  1  1  2  1 12 12  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  1 14  2 10  2  1  2  1 12  1
 0  1 11  6  5  1 11  0  1 14  1  9  3  6  1  7  4  1  1 15  4  6  1  7 15 13  1 13  8  1  1 11 10 13  1  4  1  1  0  9  1  9  1  1 13 15 15  9  2  0 12 10 12  5  2  4  2 10  6 11  9  0 11  1  1  1  1 15  1  9  1  8
 0  0 12  0  0  0  0 12  4  4 12  8  4  8  8 12  4  4 12 12  8 12  8  8  4  0  8  4 12  8  4  8  4  4  8  8  4  0  0 12  8 12 12  4  0  4  0  0  0 12  0  0 12  4 12  8 12  0 12  0  4 12  4  8  4 12  8  4  0 12 12  0
 0  0  0 12  8  4  4 12  4  8  0  0  4  8  8  8  0  4  8  4 12 12  4  4 12  4 12  0  8  0 12  8 12  4 12  0  0  4  4 12  0  0  4  8 12  8  0  0  8  4  8 12  0  8  0  4  4  0 12  8  4  0  8 12  8 12  4  0  0  4 12 12

generates a code of length 72 over Z16 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+108x^67+270x^68+536x^69+474x^70+532x^71+379x^72+508x^73+414x^74+480x^75+192x^76+124x^77+34x^78+16x^79+15x^80+6x^82+2x^84+3x^88+2x^96

The gray image is a code over GF(2) with n=576, k=12 and d=268.
This code was found by Heurico 1.16 in 0.54 seconds.