The generator matrix

 1  0  1  1  1  1  1  1  1  1  0  1  1  1  2  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  0  1 2a 2a  1  1
 0  1  1  a a+1  0 2a+3 a+1  2  a  1 2a+3 a+2 a+3  1  2  1 a+2 a+3  1  0  2 2a 2a 2a+3 2a+1 2a+1 2a+1  a a+2 3a a+1  1 a+3  1  1 3a+1 3a
 0  0 2a+2 2a  2  2  0 2a+2 2a 2a+2 2a+2  2  0 2a 2a 2a+2 2a  2  0  2 2a  2  0 2a+2 2a 2a+2  2  0  0 2a+2  2  0 2a 2a+2  2  0 2a 2a

generates a code of length 38 over GR(16,4) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+84x^109+216x^110+27x^112+180x^113+216x^114+18x^116+60x^117+72x^118+12x^120+60x^121+72x^122+6x^124

The gray image is a code over GF(4) with n=152, k=5 and d=109.
This code was found by Heurico 1.16 in 0.484 seconds.