The generator matrix

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

generates a code of length 55 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+144x^161+252x^162+27x^164+144x^165+288x^166+27x^168+60x^169+6x^172+24x^173+12x^177+36x^178+3x^188

The gray image is a linear code over GF(4) with n=220, k=5 and d=161.
This code was found by Heurico 1.16 in 1.27 seconds.