The generator matrix

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

generates a code of length 43 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 118.

Homogenous weight enumerator: w(x)=1x^0+324x^118+312x^119+228x^120+228x^121+1284x^122+888x^123+609x^124+360x^125+1992x^126+1224x^127+624x^128+396x^129+1548x^130+936x^131+585x^132+324x^133+1608x^134+864x^135+426x^136+192x^137+768x^138+384x^139+72x^140+36x^141+156x^142+9x^144+3x^156+3x^164

The gray image is a linear code over GF(4) with n=172, k=7 and d=118.
This code was found by Heurico 1.16 in 0.579 seconds.