The generator matrix

 1  0  0  1  1  1  2  1  1  8  1  1 14  4  0 12  1  1
 0  1  0  2  5  7  1  0  9  1  6  4  1  1  1  1 13  3
 0  0  1  1  3  2  1  6  5  2  6  7  4  4  5  5  4  0
 0  0  0  8  0  0  8  0  0  8  0  8  8  0  8  0  8  0
 0  0  0  0  8  0  8  8  0  0  8  8  0  0  0  8  0  8
 0  0  0  0  0  8  8  8  0  8  0  8  0  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+16x^13+382x^14+1024x^15+3711x^16+5872x^17+10756x^18+5872x^19+3748x^20+1024x^21+310x^22+16x^23+28x^24+8x^26

The gray image is a code over GF(2) with n=144, k=15 and d=52.
This code was found by Heurico 1.16 in 1.52 seconds.