The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1 aX  0  1  X (a+1)X  X  1  0  1  1  1  1  1  1  1  1 aX  1  1  X
 0  1  0 (a+1)X  X aX  1 (a+1)X+a a+1 (a+1)X+1 X+1  1 X+a+1 aX+1 (a+1)X+a+1 X+a a+1 X+a+1  a aX  1 X+a  1  1  0 (a+1)X+a  1  a a+1 (a+1)X aX aX+a X+a+1  X aX+a+1  1 X+a  0  1
 0  0  1  1 (a+1)X+a (a+1)X+a+1 a+1 aX+a+1 X+a+1 X+a X+1 X+a+1 aX+a (a+1)X  0 aX+1 aX (a+1)X+1  a  1 (a+1)X+a  X X+a  a  1 aX X+1  0  X aX a+1 (a+1)X+a aX+1 aX+a+1  1 (a+1)X+1 X+a  X (a+1)X+1

generates a code of length 39 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+1656x^112+720x^116+1008x^120+432x^124+279x^128

The gray image is a linear code over GF(4) with n=156, k=6 and d=112.
This code was found by Heurico 1.16 in 137 seconds.