The generator matrix

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

generates a code of length 55 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+372x^146+312x^147+528x^148+1116x^149+2388x^150+1752x^151+1791x^152+3684x^153+6456x^154+4332x^155+3948x^156+7188x^157+11916x^158+7944x^159+6459x^160+12252x^161+19416x^162+11472x^163+9075x^164+16164x^165+24024x^166+13908x^167+9804x^168+15180x^169+20808x^170+10524x^171+6435x^172+9276x^173+10332x^174+4416x^175+2454x^176+2484x^177+2388x^178+624x^179+378x^180+240x^181+204x^182+12x^183+33x^184+21x^188+9x^192+9x^196+6x^200+6x^204+3x^208

The gray image is a linear code over GF(4) with n=220, k=9 and d=146.
This code was found by Heurico 1.16 in 207 seconds.