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

generates a code of length 66 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+153x^56+338x^58+32x^59+512x^60+200x^61+954x^62+864x^63+1932x^64+2008x^65+2592x^66+1888x^67+1932x^68+952x^69+876x^70+160x^71+405x^72+40x^73+266x^74+156x^76+90x^78+28x^80+4x^82+1x^96

The gray image is a code over GF(2) with n=528, k=14 and d=224.
This code was found by Heurico 1.16 in 7.76 seconds.