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

generates a code of length 73 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+154x^68+64x^70+64x^71+601x^72+384x^73+448x^74+64x^75+204x^76+45x^80+18x^84+1x^136

The gray image is a code over GF(2) with n=584, k=11 and d=272.
This code was found by Heurico 1.16 in 63.2 seconds.