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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+70x^69+92x^70+142x^71+208x^72+280x^73+410x^74+578x^75+834x^76+1026x^77+1111x^78+1014x^79+821x^80+530x^81+330x^82+258x^83+138x^84+64x^85+68x^86+64x^87+29x^88+38x^89+30x^90+20x^91+16x^92+8x^93+5x^94+4x^95+2x^98+1x^120

The gray image is a code over GF(2) with n=624, k=13 and d=276.
This code was found by Heurico 1.16 in 2.59 seconds.