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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+40x^68+75x^70+8x^71+98x^72+32x^73+100x^74+74x^75+89x^76+130x^77+338x^78+168x^79+830x^80+4280x^81+841x^82+188x^83+316x^84+140x^85+67x^86+64x^87+63x^88+24x^89+66x^90+10x^91+53x^92+2x^93+28x^94+31x^96+16x^98+10x^100+4x^102+1x^104+4x^108+1x^130

The gray image is a code over GF(2) with n=648, k=13 and d=272.
This code was found by Heurico 1.16 in 3.28 seconds.