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

generates a code of length 83 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+45x^70+83x^72+104x^74+139x^76+188x^78+224x^80+512x^81+253x^82+5120x^83+294x^84+512x^85+244x^86+162x^88+91x^90+60x^92+56x^94+31x^96+27x^98+18x^100+11x^102+10x^104+5x^106+1x^108+1x^136

The gray image is a code over GF(2) with n=664, k=13 and d=280.
This code was found by Heurico 1.16 in 3.47 seconds.