The generator matrix

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

generates a code of length 43 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+87x^124+144x^125+96x^126+213x^128+120x^129+72x^130+99x^132+108x^133+27x^136+24x^138+15x^140+12x^141+3x^144+3x^156

The gray image is a linear code over GF(4) with n=172, k=5 and d=124.
This code was found by Heurico 1.16 in 0 seconds.