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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+444x^161+504x^162+240x^163+9x^164+468x^165+528x^166+144x^167+27x^168+324x^169+324x^170+72x^171+21x^172+132x^173+180x^174+60x^175+288x^177+84x^178+48x^179+72x^181+108x^182+12x^183+6x^188

The gray image is a linear code over GF(4) with n=224, k=6 and d=161.
This code was found by Heurico 1.16 in 24.3 seconds.