The generator matrix

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

generates a code of length 18 over Z16 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+16x^13+189x^14+344x^15+941x^16+1556x^17+2099x^18+1584x^19+944x^20+312x^21+155x^22+24x^23+18x^24+4x^25+5x^26

The gray image is a code over GF(2) with n=144, k=13 and d=52.
This code was found by Heurico 1.16 in 0.272 seconds.