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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+70x^60+110x^61+184x^62+258x^63+377x^64+392x^65+492x^66+744x^67+1210x^68+2066x^69+3207x^70+4700x^71+5312x^72+4526x^73+3249x^74+2164x^75+1212x^76+706x^77+476x^78+334x^79+308x^80+212x^81+151x^82+100x^83+76x^84+46x^85+45x^86+20x^87+10x^88+6x^89+3x^90+1x^114

The gray image is a code over GF(2) with n=576, k=15 and d=240.
This code was found by Heurico 1.16 in 31.9 seconds.