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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+62x^68+128x^69+264x^70+358x^71+546x^72+776x^73+1242x^74+1810x^75+2333x^76+3248x^77+3617x^78+3940x^79+3883x^80+3140x^81+2506x^82+1682x^83+1146x^84+820x^85+460x^86+270x^87+182x^88+120x^89+75x^90+50x^91+35x^92+20x^93+25x^94+16x^95+4x^96+4x^97+2x^99+2x^102+1x^106

The gray image is a code over GF(2) with n=632, k=15 and d=272.
This code was found by Heurico 1.16 in 28.9 seconds.