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

generates a code of length 66 over Z16 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+56x^58+32x^59+97x^60+80x^61+113x^62+272x^63+424x^64+640x^65+716x^66+640x^67+412x^68+272x^69+80x^70+80x^71+72x^72+32x^73+47x^74+7x^76+6x^78+7x^80+4x^82+4x^84+1x^90+1x^110

The gray image is a code over GF(2) with n=528, k=12 and d=232.
This code was found by Heurico 1.16 in 2.89 seconds.