The generator matrix

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

generates a code of length 43 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+192x^121+144x^122+120x^123+393x^124+576x^125+168x^126+228x^127+411x^128+384x^129+72x^130+72x^131+198x^132+288x^133+72x^134+132x^135+117x^136+192x^137+120x^138+24x^139+90x^140+96x^141+3x^144+3x^148

The gray image is a linear code over GF(4) with n=172, k=6 and d=121.
This code was found by Heurico 1.16 in 0.0424 seconds.