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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+43x^66+104x^68+238x^70+1233x^72+256x^73+52x^74+40x^76+34x^78+21x^80+17x^82+8x^84+1x^136

The gray image is a code over GF(2) with n=576, k=11 and d=264.
This code was found by Heurico 1.16 in 6.71 seconds.