The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+51x^68+150x^69+268x^70+558x^71+609x^72+1066x^73+733x^74+1306x^75+768x^76+1098x^77+612x^78+546x^79+220x^80+118x^81+43x^82+22x^83+8x^84+3x^86+2x^88+4x^90+1x^92+4x^96+1x^110

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 1.23 seconds.