The generator matrix

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

generates a code of length 42 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+1116x^120+1296x^124+759x^128+336x^132+588x^136

The gray image is a linear code over GF(4) with n=168, k=6 and d=120.
This code was found by Heurico 1.16 in 6.33 seconds.