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

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

Homogenous weight enumerator: w(x)=1x^0+47x^78+68x^79+141x^80+166x^81+259x^82+314x^83+349x^84+558x^85+713x^86+1170x^87+1563x^88+1796x^89+2153x^90+1840x^91+1577x^92+1254x^93+685x^94+528x^95+294x^96+254x^97+147x^98+146x^99+112x^100+58x^101+59x^102+26x^103+37x^104+8x^105+20x^106+4x^107+17x^108+2x^109+8x^110+4x^112+4x^114+1x^116+1x^122

The gray image is a code over GF(2) with n=720, k=14 and d=312.
This code was found by Heurico 1.16 in 12.5 seconds.