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

generates a code of length 65 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+74x^55+112x^56+178x^57+230x^58+286x^59+481x^60+644x^61+994x^62+1548x^63+2294x^64+2760x^65+2390x^66+1586x^67+956x^68+612x^69+368x^70+256x^71+168x^72+118x^73+96x^74+78x^75+75x^76+40x^77+13x^78+8x^79+9x^80+4x^82+2x^83+2x^87+1x^94

The gray image is a code over GF(2) with n=520, k=14 and d=220.
This code was found by Heurico 1.16 in 7.61 seconds.