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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+105x^38+8x^39+140x^40+128x^41+417x^42+496x^43+393x^44+128x^45+125x^46+8x^47+58x^48+23x^50+15x^52+2x^54+1x^72

The gray image is a code over GF(2) with n=344, k=11 and d=152.
This code was found by Heurico 1.16 in 1.29 seconds.