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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+153x^74+216x^76+104x^77+289x^78+360x^79+674x^80+592x^81+668x^82+400x^83+272x^84+72x^85+114x^86+8x^87+64x^88+47x^90+32x^92+9x^94+15x^96+3x^100+2x^104+1x^132

The gray image is a code over GF(2) with n=648, k=12 and d=296.
This code was found by Heurico 1.16 in 39.2 seconds.