The generator matrix

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

generates a code of length 55 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+588x^154+696x^155+174x^156+1536x^158+1284x^159+201x^160+2088x^162+1176x^163+213x^164+1980x^166+1188x^167+216x^168+1704x^170+1044x^171+93x^172+1044x^174+552x^175+90x^176+276x^178+204x^179+18x^180+12x^184+3x^188+3x^196

The gray image is a linear code over GF(4) with n=220, k=7 and d=154.
This code was found by Heurico 1.16 in 13.1 seconds.