The generator matrix

 1  0  1  1  1 12  1  1 10  1  1  6  1  1  6  1  2  1
 0  1  1 12 11  1  2  7  1  6  5  1  8 10  1  6  1  4
 0  0  2  6  4  6  2  2  6  0  0 14 12  6  0 14 10  2
 0  0  0  8  0  0  8  0  0  8  8  8  8  0  8  0  8  8
 0  0  0  0  8  0  8  8  8  8  0  8  0  0  0  0  8  8
 0  0  0  0  0  8  0  0  8  0  0  8  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+46x^13+180x^14+402x^15+1800x^16+3148x^17+5244x^18+3132x^19+1835x^20+382x^21+140x^22+50x^23+11x^24+8x^25+4x^26+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 1.28 seconds.