The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+22x^33+67x^34+120x^35+159x^36+268x^37+198x^38+596x^39+784x^40+1756x^41+1878x^42+4688x^43+1876x^44+1768x^45+789x^46+648x^47+177x^48+254x^49+115x^50+88x^51+59x^52+28x^53+20x^54+4x^55+14x^56+4x^58+2x^60+1x^62

The gray image is a code over GF(2) with n=344, k=14 and d=132.
This code was found by Heurico 1.16 in 5.54 seconds.