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

generates a code of length 42 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+144x^121+84x^122+120x^123+33x^124+252x^125+48x^126+18x^128+120x^129+36x^130+72x^131+12x^133+24x^134+9x^136+48x^137+3x^148

The gray image is a linear code over GF(4) with n=168, k=5 and d=121.
This code was found by Heurico 1.16 in -1.01e-007 seconds.