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

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

Homogenous weight enumerator: w(x)=1x^0+34x^68+52x^69+84x^70+144x^71+207x^72+260x^73+455x^74+606x^75+561x^76+584x^77+412x^78+234x^79+159x^80+92x^81+56x^82+28x^83+52x^84+22x^85+8x^86+10x^87+9x^88+12x^89+6x^90+2x^91+1x^92+2x^93+2x^98+1x^122

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 0.796 seconds.