The generator matrix

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

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+93x^112+144x^113+96x^114+216x^116+96x^117+72x^118+90x^120+144x^121+18x^124+24x^126+24x^128+6x^140

The gray image is a linear code over GF(4) with n=156, k=5 and d=112.
This code was found by Heurico 1.16 in 0.016 seconds.