The generator matrix

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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+68x^32+54x^34+30x^35+205x^36+60x^37+172x^38+178x^39+484x^40+380x^41+1680x^42+596x^43+4494x^44+4888x^45+6179x^46+4900x^47+4427x^48+632x^49+1769x^50+358x^51+417x^52+172x^53+266x^54+74x^55+122x^56+12x^57+90x^58+8x^59+20x^60+23x^62+2x^64+7x^66

The gray image is a code over GF(2) with n=368, k=15 and d=128.
This code was found by Heurico 1.16 in 15.8 seconds.