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

generates a code of length 82 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+52x^68+41x^70+8x^71+101x^72+8x^73+70x^74+78x^75+96x^76+148x^77+87x^78+498x^79+67x^80+808x^81+4171x^82+804x^83+64x^84+480x^85+62x^86+132x^87+52x^88+80x^89+74x^90+14x^91+29x^92+12x^93+50x^94+2x^95+34x^96+31x^98+14x^100+15x^102+1x^104+6x^106+1x^108+1x^126

The gray image is a code over GF(2) with n=656, k=13 and d=272.
This code was found by Heurico 1.16 in 3.31 seconds.