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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+169x^76+112x^78+256x^79+233x^80+512x^81+256x^82+256x^83+154x^84+16x^86+69x^88+13x^92+1x^152

The gray image is a code over GF(2) with n=648, k=11 and d=304.
This code was found by Heurico 1.16 in 1.14 seconds.