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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+170x^62+16x^63+353x^64+40x^65+628x^66+248x^67+980x^68+936x^69+1770x^70+1864x^71+2533x^72+1800x^73+1937x^74+904x^75+802x^76+280x^77+460x^78+40x^79+276x^80+16x^81+176x^82+97x^84+40x^86+13x^88+3x^90+1x^100

The gray image is a code over GF(2) with n=576, k=14 and d=248.
This code was found by Heurico 1.16 in 8.85 seconds.