The generator matrix

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

generates a code of length 55 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+312x^150+396x^151+498x^152+1068x^153+1644x^154+1392x^155+1908x^156+1884x^157+2736x^158+2484x^159+2607x^160+2916x^161+3756x^162+2940x^163+3105x^164+3360x^165+4620x^166+3732x^167+3141x^168+3276x^169+4032x^170+3000x^171+2403x^172+2052x^173+2244x^174+1260x^175+1038x^176+708x^177+600x^178+156x^179+135x^180+96x^181+24x^182+3x^184+9x^188

The gray image is a linear code over GF(4) with n=220, k=8 and d=150.
This code was found by Heurico 1.16 in 15.1 seconds.