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

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

Homogenous weight enumerator: w(x)=1x^0+189x^68+140x^69+404x^70+384x^71+765x^72+756x^73+1016x^74+1024x^75+1007x^76+756x^77+682x^78+384x^79+316x^80+140x^81+130x^82+35x^84+18x^86+18x^88+22x^90+3x^92+1x^100+1x^108

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 2.63 seconds.