The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+148x^31+509x^32+584x^33+1315x^34+1714x^35+2775x^36+2334x^37+2867x^38+1670x^39+1267x^40+542x^41+385x^42+142x^43+85x^44+26x^45+9x^46+6x^47+3x^48+2x^49

The gray image is a code over GF(2) with n=296, k=14 and d=124.
This code was found by Heurico 1.16 in 2.34 seconds.