The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+171x^68+200x^69+722x^70+784x^71+1585x^72+1496x^73+2470x^74+1696x^75+2444x^76+1496x^77+1486x^78+784x^79+627x^80+200x^81+110x^82+46x^84+32x^86+12x^88+12x^90+6x^92+3x^96+1x^108

The gray image is a code over GF(2) with n=600, k=14 and d=272.
This code was found by Heurico 1.16 in 6.86 seconds.