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  0  1  1  1  1  2 12  1  1  1  1  2  1  1  1  1  8  2  0  1  1  0  1  1  1  1  2  8  2  2  1  1  1  8  2  2  4  2  1  2  8  2 12  0  4  1 12  1  1
 0  2  0  2  0  0  6 14  4  4 10  6 12  6 10  4 12  4  2  4 14  4  6 10  8  4 10 14  0  2 10  8 14  4  0  8  8  6  0  2 14 10  8 10  6  2 12  8 14  4  2 14  8  8  8 12  2  2 14 12  4  2  8 14  6  2  2  8  2  2 12  0 12  2 12  2 10 14
 0  0  2  2 12  6  6  4  4  2  6  0  8 10  4 14 10  4  6  6 10  0  0  0 14 12  4 14 14  8  2  8 12 14  6  2 12 12  8  2 12 10  2  2  0 12 10  2  6 10  0  4 14  4  4  6 10 10  2  0  8  0  2  2 14  2 10 10  0 10  2  2  2 12 14 10 14 10
 0  0  0  8  0  0  8  0  0  0  8  8  8  0  8  8  0  8  0  8  0  0  0  8  8  8  0  0  8  8  8  8  8  8  8  8  0  8  0  0  8  0  0  8  0  0  0  0  8  8  0  8  0  8  8  0  0  8  8  8  0  0  8  0  8  0  8  8  8  0  8  8  8  0  0  8  0  8
 0  0  0  0  8  0  8  0  8  8  0  0  0  8  0  0  8  8  0  0  8  0  8  8  8  0  8  0  8  0  8  8  8  8  8  0  8  0  8  8  0  0  8  0  0  0  8  8  0  0  8  0  8  0  8  0  0  0  0  8  8  8  8  0  8  8  0  0  8  8  0  0  8  8  8  0  8  0
 0  0  0  0  0  8  0  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  8  0  8  8  0  0  0  8  8  8  8  8  8  0  8  8  0  0  0  0  0  8  0  8  0  8  0  0  8  0  0  0  8  8  8  0  8  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+80x^71+242x^72+488x^73+496x^74+740x^75+673x^76+1130x^77+812x^78+992x^79+714x^80+638x^81+390x^82+306x^83+150x^84+146x^85+80x^86+54x^87+6x^88+26x^89+14x^90+2x^91+4x^92+4x^93+2x^95+1x^96+1x^108

The gray image is a code over GF(2) with n=624, k=13 and d=284.
This code was found by Heurico 1.16 in 1.85 seconds.