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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+116x^78+16x^79+288x^80+64x^81+493x^82+196x^83+759x^84+728x^85+1024x^86+1080x^87+1001x^88+688x^89+663x^90+232x^91+323x^92+56x^93+179x^94+8x^95+130x^96+62x^98+4x^99+41x^100+21x^102+16x^104+2x^106+1x^132

The gray image is a code over GF(2) with n=696, k=13 and d=312.
This code was found by Heurico 1.16 in 3.06 seconds.