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

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

Homogenous weight enumerator: w(x)=1x^0+121x^76+102x^78+32x^79+174x^80+1216x^81+162x^82+32x^83+95x^84+82x^86+21x^88+6x^90+3x^92+1x^156

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 12.1 seconds.