The generator matrix

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

generates a code of length 41 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+38x^30+14x^31+76x^32+86x^33+121x^34+178x^35+264x^36+434x^37+589x^38+2884x^39+964x^40+5092x^41+972x^42+2876x^43+597x^44+460x^45+248x^46+174x^47+105x^48+70x^49+57x^50+18x^51+34x^52+2x^53+21x^54+6x^56+2x^58+1x^60

The gray image is a code over GF(2) with n=328, k=14 and d=120.
This code was found by Heurico 1.16 in 3.96 seconds.