The generator matrix

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

generates a code of length 39 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+816x^111+384x^112+936x^115+204x^116+552x^119+288x^120+504x^123+72x^124+264x^127+63x^128+12x^132

The gray image is a linear code over GF(4) with n=156, k=6 and d=111.
This code was found by Heurico 1.16 in 0.401 seconds.