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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  4  2  4  4  2  1  1  1  4  2  2  8  1  1  1  2  1  8  1  1  4  4  1  0  1  2  2  1  1  1  2  1  1  2  1  4  2  1
 0 12  0  0  0  0  0  0  0 12 12  4  4  4  4  4  0 12  8  4 12  4  4  8  4  0  8  8 12 12  8  4  4  4 12  0  8  8  0  8  8  4  8  4  4  8  4  0  8 12 12  8  4 12  0 12  4  0  4  0 12  4  0 12 12  4  0  8  0  0  8  4  0  0  4  4  4  4 12  8 12  8 12  4  0  0 12  8  0
 0  0 12  0  0  0  4 12  4  4 12  8  4  8  8  4  0  4  8  8 12 12  0  4  8  8  4  4  0 12 12  8 12 12  0  0  8  8  8 12  4 12 12 12 12  0  0  8  4  8  0  4 12  0  0  0 12  8  4  4  8  8  4 12  8  0  4  0  4  8 12  8  8 12 12 12  4  4 12  4 12  0  4 12  0 12  0  8  0
 0  0  0 12  0  4  4 12  0  8 12 12 12 12  8  0 12  0  0 12  4  4 12  0 12  8 12  4  8  8  0  0  4  8  4  4 12  8  4  8 12  4  0  8  8 12  8  0  8  8  8  0  0  8  8 12 12  0 12 12  0  0 12  4  8  4  0  8  4 12  0  0 12 12 12  0  8  4  0  8 12 12  0  0  0  0  8 12  0
 0  0  0  0 12  4  0 12  4 12  8  4 12  8 12  0  4  4  4  4  4  8  0 12  8  0 12  0  8  8 12  4  8  4  0  0  0  8 12  8  8 12  8  0  0 12  0  4  0  0  0  8  0  0  4  4 12  4  0  8 12 12  0 12  0  0  8  4  8  8  4 12 12  4  0 12 12  8 12 12 12 12  8  8 12 12  8  0  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  8  0  0  8  0  8  8  0  0  8  0  0  0  8  8  8  0  0  0  8  0  0  8  8  8  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  8  8  0  0  8  0  0  8  0  0  8  8  8  0  8  0  0  8  0  8  0  8  0  8  8  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  0  8  8  8  8  0  8  0  0  8  8  0  8  0  0  8  0  8  0  8  0  8  8  0  8  8  8  8  0  0  0  0  0  0  8  8  0  0  8  0  0  0  0  8  8  8  0  8  8  8  8  0  8  0  0  0  0  0  8  0  8  8  8  8  8  0  0  0  0  8  8  0  8
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  0  8  0  8  8  0  8  0  0  0  8  0  8  0  0  8  8  0  8  8  8  0  8  0  8  0  0  8  0  8  0  0  8  0  8  0  0  0  0  8  8  8  0  8  8  8  8  8  8  0  8  8  8  0  0  0  8  8  0  8  8  8  8  0  0  0  0  8  8

generates a code of length 89 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+59x^76+112x^77+164x^78+222x^79+340x^80+378x^81+555x^82+694x^83+940x^84+1484x^85+2242x^86+3214x^87+3936x^88+4346x^89+3936x^90+3098x^91+2252x^92+1440x^93+941x^94+688x^95+439x^96+316x^97+236x^98+224x^99+174x^100+90x^101+98x^102+44x^103+42x^104+24x^105+16x^106+8x^107+7x^108+2x^109+3x^110+2x^112+1x^130

The gray image is a code over GF(2) with n=712, k=15 and d=304.
This code was found by Heurico 1.16 in 42.7 seconds.