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

generates a code of length 76 over Z16 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+56x^67+329x^68+740x^69+956x^70+1370x^71+1872x^72+2644x^73+2911x^74+3910x^75+3466x^76+4028x^77+2785x^78+2610x^79+1800x^80+1328x^81+752x^82+436x^83+295x^84+200x^85+136x^86+58x^87+38x^88+20x^89+9x^90+6x^91+6x^92+3x^94+2x^95+1x^96

The gray image is a code over GF(2) with n=608, k=15 and d=268.
This code was found by Heurico 1.16 in 22.6 seconds.