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  8  1  1  1  1  1  1  1  1  1  1  1  1  4  1  1  1  8  1  1  1  1  1  1  1  1  1  1  2  1  4  1  1  4  0  1  1  1  1  1  1  8  4  2  2  0  1  2
 0  2  0  6  4 14 12  2  8  6  6 12  2  0 10 12  0  6 12 10 14  8  4  2  0  6  6 12  0  2 12  2  8  2  0 14 10 10 10 12 12 10  6  4  8  6  2  2 14  0  2  8  0  0 14 10 12  6  8  6 14  8  8  4 12  4  2  2  2  0 12  0  4  4  4  2  6 10  2 10 14
 0  0 12  0  4  4  8  4  4  0 12  0 12  8  0 12  0  0  8  8  4  4 12 12 12  0 12 12  8  8  0  4 12  4 12 12  8 12  4  0  4  0  8 12  0 12 12  8  8  4 12  0  8  4  4  8  0  4  4  0  4 12  4  0  0  0 12  8  4  8  4  8  0  4  4  4  0  8  0  8 12
 0  0  0  8  0  0  8  8  0  8  0  8  8  0  0  0  0  0  8  0  0  8  8  0  8  8  8  8  8  8  0  8  8  8  0  0  8  0  8  0  0  8  0  0  8  8  8  8  8  8  0  8  8  8  8  0  0  8  8  0  0  8  0  0  8  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8
 0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  0  8  8  0  0  0  8  8  0  0  8  8  8  8  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  8  0  0  8  0  0  8  8  0  8  0  8  0  0  8  8  8  8  0  8  8  0  0  8  8  8  0  0  8  0
 0  0  0  0  0  8  0  8  8  8  0  8  0  8  8  8  8  8  0  0  0  0  8  8  8  8  0  0  8  0  0  8  0  8  8  0  8  8  0  0  0  0  8  0  0  8  0  8  0  0  8  8  8  8  0  8  8  8  8  0  0  8  8  0  0  8  0  8  8  0  0  0  8  8  8  0  0  0  0  0  8

generates a code of length 81 over Z16 who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+108x^75+215x^76+284x^77+172x^78+480x^79+584x^80+552x^81+552x^82+316x^83+396x^84+156x^85+44x^86+120x^87+47x^88+32x^89+29x^92+7x^96+1x^136

The gray image is a code over GF(2) with n=648, k=12 and d=300.
This code was found by Heurico 1.16 in 56.2 seconds.