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

generates a code of length 83 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+16x^69+80x^70+66x^71+226x^72+180x^73+273x^74+420x^75+303x^76+760x^77+504x^78+1668x^79+1058x^80+4140x^81+3760x^82+5936x^83+3707x^84+4210x^85+1029x^86+1698x^87+525x^88+756x^89+299x^90+364x^91+218x^92+148x^93+133x^94+72x^95+63x^96+28x^97+50x^98+16x^99+27x^100+2x^101+12x^102+15x^104+2x^106+1x^108+1x^110+1x^118

The gray image is a code over GF(2) with n=664, k=15 and d=276.
This code was found by Heurico 1.16 in 40 seconds.