The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^13+109x^14+136x^15+308x^16+846x^17+1225x^18+848x^19+291x^20+122x^21+103x^22+40x^23+7x^24+10x^25+3x^26+1x^28

The gray image is a code over GF(2) with n=144, k=12 and d=52.
This code was found by Heurico 1.16 in 0.126 seconds.