The generator matrix

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

generates a code of length 43 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+780x^119+570x^120+2484x^123+732x^124+2952x^127+1029x^128+3000x^131+993x^132+2028x^135+420x^136+1044x^139+333x^140+6x^144+3x^148+6x^152+3x^156

The gray image is a linear code over GF(4) with n=172, k=7 and d=119.
This code was found by Heurico 1.16 in 30.6 seconds.