The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^13+177x^14+306x^15+807x^16+1690x^17+2131x^18+1694x^19+812x^20+298x^21+151x^22+46x^23+12x^24+6x^25+5x^26+2x^27

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 0.466 seconds.