The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^14+78x^15+185x^16+444x^17+552x^18+424x^19+180x^20+68x^21+32x^22+10x^23+18x^24+1x^30

The gray image is a code over GF(2) with n=144, k=11 and d=56.
This code was found by Heurico 1.16 in 0.0184 seconds.