The generator matrix

 1  0  0  0  1  1  1  1 12  1  6  2  6  1  1  6 12  1 12  2  1 10  1  0  1  6  1  1  1  1  1 10  1 14  1  1  1  1  1  1 10 12 14  4  1  1  1  4  1  1  1 12 14  1  1  1  2 12  4 14  1  1  8  1 10  1  2  0  1  1  1 14  4  1  1 12 12  1  1 10  1
 0  1  0  0  2  5  9  4  1  6  2  1  1  9  5  1  1  2 14  4  7  1  1  8  8  1  1  0 14 11 12 14 11  1  7  1 14 11  2 12  1  1  1  1 13 10  8  1  0  6  4  0  2  6 15  0  8  6  1  1  8  4  4 10  1  1  1  1 13  1  7  1  1  3  6  8  1  0  8  1  6
 0  0  1  0  0  4  1  5  7  9  1  5 10  6  3  4  6 10  1  1  4  9  9 10 11  9 15 14  5 14 11  1 15 15  7  6 10  6  8  5 12  8  0 11  8  9  2  8 11  4  9  1 12 12  0 10  1 12 10  5  6  7  1 12  6  0 10 12 13  3 11  7  5 14 11  1 14  7  8 11  8
 0  0  0  1  1  7  4  1  7  2 13  6  7  2  3  3 12  9 14 13 14  0 10  1  1 13 13 12  4  9  3  3  6 14 11  8  3  7 10  8 12  5 10  5 10 11  9 10  6  8 13  6  1  2  5  9  5  1  8  4  6  7 14  3  7  1  9 13 13 10 15 11 14 14 13  7  0  4 14  4 11
 0  0  0  0  4  0  0  0  0  4  4  4  4 12 12 12  8 12  8  4  4  4  0  0  0  8  4  0  8  8  4  8  4  8  0  4  0 12 12  8  0 12  8  8  0  0 12  4  4 12 12  4  0  8  0  8 12 12  4 12 12  8  8 12 12 12  8  8  0  8  8  0 12  0  0  0 12 12 12  4  0

generates a code of length 81 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+295x^72+1438x^73+3305x^74+5870x^75+10002x^76+14984x^77+21892x^78+25200x^79+32853x^80+30784x^81+32479x^82+25920x^83+21834x^84+14814x^85+10024x^86+5246x^87+2814x^88+1334x^89+563x^90+308x^91+96x^92+32x^93+22x^94+10x^95+8x^96+4x^97+1x^98+6x^99+2x^101+2x^102+1x^104

The gray image is a code over GF(2) with n=648, k=18 and d=288.
This code was found by Heurico 1.16 in 728 seconds.