The generator matrix

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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+75x^152+108x^155+651x^156+204x^157+312x^159+1287x^160+360x^161+480x^163+1803x^164+552x^165+672x^167+2379x^168+1056x^169+924x^171+2322x^172+684x^173+456x^175+1248x^176+216x^177+120x^179+309x^180+54x^184+33x^188+36x^192+18x^196+18x^200+6x^208

The gray image is a linear code over GF(4) with n=224, k=7 and d=152.
This code was found by Heurico 1.16 in 1.22 seconds.