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

generates a code of length 76 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+80x^68+136x^70+28x^71+289x^72+224x^73+508x^74+524x^75+644x^76+512x^77+462x^78+212x^79+234x^80+32x^81+74x^82+4x^83+58x^84+26x^86+26x^88+10x^90+10x^92+1x^96+1x^120

The gray image is a code over GF(2) with n=608, k=12 and d=272.
This code was found by Heurico 1.16 in 0.917 seconds.