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

generates a code of length 69 over Z16 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+203x^58+536x^60+20x^61+762x^62+196x^63+1327x^64+1020x^65+2714x^66+2812x^67+4761x^68+4172x^69+4772x^70+2844x^71+2680x^72+1028x^73+1276x^74+164x^75+693x^76+32x^77+391x^78+209x^80+115x^82+30x^84+7x^86+2x^88+1x^104

The gray image is a code over GF(2) with n=552, k=15 and d=232.
This code was found by Heurico 1.16 in 33.9 seconds.