The generator matrix

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

generates a code of length 46 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+276x^129+96x^130+180x^131+75x^132+504x^133+204x^134+168x^135+96x^136+552x^137+156x^138+144x^139+27x^140+480x^141+228x^142+216x^143+24x^144+324x^145+84x^146+60x^147+9x^148+168x^149+12x^152+3x^160+6x^164+3x^172

The gray image is a linear code over GF(4) with n=184, k=6 and d=129.
This code was found by Heurico 1.16 in 5.96 seconds.