The generator matrix

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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+432x^71+1590x^72+2688x^73+4636x^74+5292x^75+6998x^76+7512x^77+7924x^78+7484x^79+6990x^80+5248x^81+3892x^82+2196x^83+1412x^84+632x^85+376x^86+116x^87+59x^88+16x^89+28x^90+12x^92+2x^96

The gray image is a code over GF(2) with n=624, k=16 and d=284.
This code was found by Heurico 1.16 in 43.1 seconds.