The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+136x^13+348x^14+812x^15+1734x^16+3102x^17+4026x^18+3234x^19+1775x^20+788x^21+264x^22+112x^23+41x^24+6x^25+2x^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 63.5 seconds.