The generator matrix

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

generates a code of length 55 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 158.

Homogenous weight enumerator: w(x)=1x^0+576x^158+468x^159+63x^160+612x^162+480x^163+96x^164+408x^166+216x^167+66x^168+300x^170+168x^171+12x^172+336x^174+132x^175+72x^178+72x^179+12x^180+6x^184

The gray image is a linear code over GF(4) with n=220, k=6 and d=158.
This code was found by Heurico 1.16 in 0.0691 seconds.