The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+52x^26+4x^27+122x^28+20x^29+202x^30+132x^31+331x^32+372x^33+694x^34+2440x^35+1582x^36+9320x^37+2192x^38+9320x^39+1622x^40+2440x^41+715x^42+372x^43+326x^44+132x^45+194x^46+20x^47+92x^48+4x^49+41x^50+18x^52+4x^54+2x^56+1x^58+1x^66

The gray image is a code over GF(2) with n=304, k=15 and d=104.
This code was found by Heurico 1.16 in 11.6 seconds.