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

generates a code of length 90 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+39x^78+92x^79+167x^80+210x^81+380x^82+636x^83+873x^84+1236x^85+1725x^86+2474x^87+3101x^88+3450x^89+3969x^90+3592x^91+3105x^92+2692x^93+1637x^94+1180x^95+768x^96+498x^97+345x^98+184x^99+117x^100+88x^101+64x^102+30x^103+39x^104+18x^105+24x^106+4x^107+15x^108+6x^110+4x^112+1x^114+2x^116+1x^118+1x^122

The gray image is a code over GF(2) with n=720, k=15 and d=312.
This code was found by Heurico 1.16 in 35.5 seconds.