The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  8  1  2  1  2  1  0  1  1  1  4  1  8  1  1  4  4  4  1  2  1  4  1
 0  2  0  6  4  6 12  2  6 14 12  4  8  2 10 14  2  2  2  6 12  2  8  2  4  6  0  2  6  2 14 12  8  2 12  0  6 12  0  0
 0  0 12  0  4  0  0  8  4 12  4  0  8  4  4  0  0 12  4  4 12  0 12  8  4  8  0  4  4 12  0  0 12  8  4  4  0  8 12  0
 0  0  0 12  0  0  0 12  4  8 12 12  4  8 12  4 12  0  8  4 12  4  8  8  0  8  8  8 12  0  4  8  4 12  4  4  0  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  0  8  0  0  8  0  0  8  8  8  8  0  8  8  8  8  8  8  0
 0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  0  0  0  0  0  8  8  8  8  8  0  8  0  0  0  8  8  8  0  8  0  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  8  8  8  0  0  8  0  0  8  8  0  0  0  8  8  0  0  8  8  0  8  8  8  0  0  0  8  0  8  8

generates a code of length 40 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+46x^32+98x^33+194x^34+398x^35+919x^36+928x^37+2246x^38+1604x^39+3376x^40+1720x^41+2469x^42+964x^43+716x^44+312x^45+176x^46+100x^47+57x^48+14x^49+32x^50+6x^51+5x^52+2x^54+1x^58

The gray image is a code over GF(2) with n=320, k=14 and d=128.
This code was found by Heurico 1.16 in 3.02 seconds.