The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+29x^26+104x^28+235x^30+32x^31+494x^32+192x^33+926x^34+2528x^35+1281x^36+4736x^37+1291x^38+2528x^39+946x^40+192x^41+486x^42+32x^43+210x^44+89x^46+31x^48+14x^50+5x^52+1x^54+1x^58

The gray image is a code over GF(2) with n=296, k=14 and d=104.
This code was found by Heurico 1.16 in 3.13 seconds.