The generator matrix

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

generates a code of length 41 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+240x^106+552x^107+849x^108+1092x^109+2172x^110+2532x^111+3792x^112+3552x^113+5928x^114+6708x^115+7704x^116+7704x^117+12036x^118+12684x^119+13728x^120+13272x^121+19248x^122+19104x^123+18834x^124+16356x^125+20820x^126+17196x^127+14541x^128+10656x^129+10872x^130+7716x^131+5430x^132+2592x^133+2412x^134+1092x^135+561x^136+72x^137+48x^140+24x^144+12x^148+9x^152+3x^156

The gray image is a linear code over GF(4) with n=164, k=9 and d=106.
This code was found by Heurico 1.16 in 164 seconds.