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

generates a code of length 76 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+27x^68+132x^69+199x^70+328x^71+380x^72+676x^73+928x^74+954x^75+1096x^76+924x^77+912x^78+634x^79+339x^80+290x^81+138x^82+118x^83+32x^84+22x^85+13x^86+6x^87+8x^88+2x^89+14x^90+8x^91+4x^92+2x^93+4x^94+1x^116

The gray image is a code over GF(2) with n=608, k=13 and d=272.
This code was found by Heurico 1.16 in 2.09 seconds.