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

generates a code of length 69 over Z16 who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+78x^59+147x^60+188x^61+236x^62+294x^63+428x^64+568x^65+979x^66+1750x^67+2294x^68+2502x^69+2399x^70+1780x^71+979x^72+512x^73+337x^74+236x^75+196x^76+140x^77+121x^78+68x^79+42x^80+48x^81+24x^82+16x^83+7x^84+10x^85+2x^87+1x^88+1x^104

The gray image is a code over GF(2) with n=552, k=14 and d=236.
This code was found by Heurico 1.16 in 30.3 seconds.