The generator matrix

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

generates a code of length 46 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+216x^134+186x^136+432x^138+48x^142+60x^144+48x^146+24x^150+6x^152+3x^160

The gray image is a linear code over GF(4) with n=184, k=5 and d=134.
This code was found by Heurico 1.16 in 1.64 seconds.