The generator matrix

 1  0  0  1  1  1 10  1  1  4  1  1 14  1  8  1  6  1
 0  1  0  4  5 11  1  2  7  1  6  3  1  9  4 13  0  1
 0  0  1  7  3  4  5  2  1  1  5  6  4  3  1  4  1  1
 0  0  0  8  0  0  0  8  8  8  0  0  8  8  0  8  8  0
 0  0  0  0  8  8  0  8  0  8  0  0  0  8  8  8  0  8

generates a code of length 18 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+106x^14+744x^15+1513x^16+3484x^17+4718x^18+3496x^19+1480x^20+704x^21+102x^22+16x^23+14x^24+4x^25+2x^26

The gray image is a code over GF(2) with n=144, k=14 and d=56.
This code was found by Heurico 1.16 in 0.444 seconds.