The generator matrix

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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+423x^160+168x^161+396x^163+633x^164+192x^165+180x^167+579x^168+144x^169+477x^172+192x^173+348x^176+72x^177+180x^179+78x^180+12x^183+3x^184+9x^188+6x^192+3x^196

The gray image is a linear code over GF(4) with n=224, k=6 and d=160.
This code was found by Heurico 1.16 in 0.095 seconds.