The generator matrix

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

generates a code of length 42 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+108x^108+372x^109+384x^110+1044x^111+1128x^112+2136x^113+2784x^114+3516x^115+3546x^116+6420x^117+5820x^118+8484x^119+8037x^120+11952x^121+11556x^122+16236x^123+12135x^124+18264x^125+17064x^126+21756x^127+14577x^128+20520x^129+15672x^130+16500x^131+10551x^132+11652x^133+7068x^134+5580x^135+2907x^136+2352x^137+1092x^138+612x^139+174x^140+60x^141+36x^144+21x^148+18x^152+9x^156

The gray image is a linear code over GF(4) with n=168, k=9 and d=108.
This code was found by Heurico 1.16 in 145 seconds.