The generator matrix

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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+390x^156+132x^157+420x^159+1671x^160+648x^161+636x^163+2142x^164+708x^165+780x^167+2187x^168+612x^169+516x^171+1836x^172+384x^173+456x^175+1320x^176+516x^177+240x^179+588x^180+72x^181+24x^183+90x^184+9x^188+3x^200+3x^204

The gray image is a linear code over GF(4) with n=224, k=7 and d=156.
This code was found by Heurico 1.16 in 0.796 seconds.