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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+112x^70+798x^72+112x^74+1x^144

The gray image is a code over GF(2) with n=576, k=10 and d=280.
This code was found by Heurico 1.16 in 1.28 seconds.