The generator matrix

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

generates a code of length 39 over GR(16,4) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+732x^111+420x^112+1080x^115+216x^116+480x^119+180x^120+552x^123+108x^124+228x^127+87x^128+12x^132

The gray image is a code over GF(4) with n=156, k=6 and d=111.
This code was found by Heurico 1.16 in 0.093 seconds.