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

generates a code of length 55 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+936x^159+465x^160+948x^163+207x^164+396x^167+108x^168+420x^171+108x^172+252x^175+114x^176+120x^179+18x^180+3x^196

The gray image is a linear code over GF(4) with n=220, k=6 and d=159.
This code was found by Heurico 1.16 in 27.9 seconds.