The generator matrix

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

generates a code of length 55 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+240x^156+156x^157+252x^159+720x^160+156x^161+156x^163+534x^164+180x^165+132x^167+504x^168+132x^169+180x^171+363x^172+96x^173+48x^175+177x^176+48x^177+6x^180+6x^184+3x^188+6x^196

The gray image is a linear code over GF(4) with n=220, k=6 and d=156.
This code was found by Heurico 1.16 in 0.0929 seconds.