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

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+612x^154+732x^155+177x^156+1548x^158+1104x^159+207x^160+1956x^162+1440x^163+204x^164+2088x^166+1092x^167+198x^168+1692x^170+1008x^171+105x^172+1068x^174+540x^175+102x^176+252x^178+228x^179+18x^180+6x^184+6x^192

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 185 seconds.