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  4  1  2  2  1  1 12  1  1  1  1  4  1  1  1  2  1  4  2  0  1  1  1  1  8  1  1  0  1  4  1  2  1  1  2  4  1  4  1  1  1  4  2  1  1  1  1  1  1
 0  2  0  2  0  8  2 10  8  2 12 14  0 10  4  6  4  6  4 14 12  2  6  0  0  2  2  2  2 12  8 10  2 12  0  6  8  2  6  4  6  4  8  0 14  2  2  6  0  0  2  6  4  2 14  2 10  0  8  2 10  4  4  0 14  6  4  2  8  2  4  8  2 10  0
 0  0  2  2 12 14  6 12  0  2 10 12  4 14 14  8  4 10 10  4  4  8  6  6 10  8 12 14 10 10  4 14  0 12  6  8  8  8 12  6  2 10  8  2 12 10 14  8  2  2  0  0  2 10 14 14  8 10 10 14  2  2  2  2  4 12  4 10  2  0  6 14 14  4  0
 0  0  0  4  0  0 12  8  4  8 12 12 12  8  4 12  8  4  8  0 12 12  0  8  4  0  8 12  8  0 12  8  8 12 12  8  8  4 12  8  0 12 12 12  0  8  0  8  4 12 12  0  4  0  8 12 12  8 12  4 12 12  8  4  8  8  0 12 12  4  8  8  4  8  0
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  0  0  8  0  0  8  0  8  8  8  8  0  0  8  0  0  0  8  0  0  0  8  8  0  0  0  8  0  0  8  0  8  8  0  8  0  8  8  0  8  0  8  8  0  0  0  0  8  0  0  8  0  8  0  8  8  8  8  8  8

generates a code of length 75 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+70x^68+214x^69+324x^70+488x^71+658x^72+912x^73+1109x^74+1044x^75+1021x^76+824x^77+503x^78+340x^79+206x^80+138x^81+126x^82+100x^83+41x^84+16x^85+29x^86+12x^87+3x^88+6x^89+4x^90+2x^93+1x^114

The gray image is a code over GF(2) with n=600, k=13 and d=272.
This code was found by Heurico 1.16 in 1.86 seconds.