The generator matrix

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

generates a code of length 31 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+81x^26+16x^27+118x^28+192x^29+450x^30+352x^31+450x^32+192x^33+96x^34+16x^35+66x^36+6x^38+4x^40+7x^42+1x^48

The gray image is a code over GF(2) with n=248, k=11 and d=104.
This code was found by Heurico 1.16 in 59.5 seconds.