The generator matrix

 1  0  1  1  1 14  1  1  8  1 10  1  1  6  8  1  4  2
 0  1 11  6  1  1  3  8  1 10  1  0 13  1  2  4  4 14
 0  0 12  0  0  0  0  4  4 12 12  8 12  4  8  0  4 12
 0  0  0 12  0  4  4  4 12  8  8  4 12 12  0 12  0 12
 0  0  0  0  4  8 12  4  4 12  4  4  4  0 12  8  8 12

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

Homogenous weight enumerator: w(x)=1x^0+78x^13+264x^14+702x^15+1852x^16+3290x^17+3964x^18+3366x^19+1867x^20+690x^21+216x^22+58x^23+23x^24+6x^25+4x^26+2x^27+1x^28

The gray image is a code over GF(2) with n=144, k=14 and d=52.
This code was found by Heurico 1.16 in 0.597 seconds.