The generator matrix

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

generates a code of length 46 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+87x^116+291x^120+384x^124+444x^128+1155x^132+5091x^136+7362x^140+432x^144+441x^148+294x^152+210x^156+120x^160+57x^164+12x^168+3x^176

The gray image is a linear code over GF(4) with n=184, k=7 and d=116.
This code was found by Heurico 1.16 in 1.91 seconds.