The generator matrix

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

generates a code of length 47 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 131.

Homogenous weight enumerator: w(x)=1x^0+996x^131+588x^132+2412x^135+792x^136+2964x^139+852x^140+2532x^143+975x^144+2280x^147+654x^148+960x^151+213x^152+144x^155+12x^156+6x^164+3x^168

The gray image is a linear code over GF(4) with n=188, k=7 and d=131.
This code was found by Heurico 1.16 in 35.3 seconds.