The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  2  1  1  4  1  1  2
 0 12  0  0  0  4 12 12  8  8  4  0  0  8 12 12 12  0
 0  0 12  0  4  4  4  0  8  0 12  4  4  0  4  4  8 12
 0  0  0 12  4  8  4  4  0  4  8 12 12  4 12  0  4  0
 0  0  0  0  8  8  0  8  8  8  8  8  0  0  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+89x^14+32x^15+112x^16+480x^17+641x^18+480x^19+91x^20+32x^21+67x^22+19x^24+3x^26+1x^28

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 0.0321 seconds.