The generator matrix

 1  0  0  1  1  1 14  1  1  1  1  1 10  1  0  1  0  1
 0  1  0  1  6  7  1  8  4  5  1  4  1  1  2 13  1  0
 0  0  1  1  3  2  3  0  7  4  7  3  2  1  1 13  5  0
 0  0  0 12  0  8 12  4  8 12  0 12  4  0 12  4  8  0
 0  0  0  0  8  8  8  0  0  8  0  8  0  8  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+42x^13+380x^14+1092x^15+3330x^16+6314x^17+10257x^18+6656x^19+3330x^20+934x^21+334x^22+60x^23+27x^24+6x^25+5x^26

The gray image is a code over GF(2) with n=144, k=15 and d=52.
This code was found by Heurico 1.16 in 1.69 seconds.