The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 (a+1)X  1  0  1  1  1 (a+1)X aX  1  1  1  1  1 aX  1  0  1  1  X  1  1  1  1  1  1  X  1  1  X (a+1)X (a+1)X  1  1  0  X  1  1  1 aX  1  1  1
 0  1  0  0  0 (a+1)X  1 (a+1)X+a a+1 (a+1)X+1  1 (a+1)X+a  a (a+1)X+a+1  1 (a+1)X+a+1  1 (a+1)X+1 a+1  a  1  1 (a+1)X+a+1 a+1  0 aX X+1  1 (a+1)X+a (a+1)X  a  1  1 aX+a+1 aX+a  1 X+a+1 aX a+1  1 (a+1)X+1 aX  1  1  1 (a+1)X+a+1  a  1  1 X+1 X+a  X  1  1  a  0
 0  0  1  1  a a+1  1 X+1  1  0 a+1 X+a+1  a aX+a X+1 aX  a  a a+1  X X+a+1  0 X+1 (a+1)X+a (a+1)X+a  X  X X+1 aX+1  1 X+a X+a+1 X+a aX+a+1  a  0 (a+1)X  1 aX+a+1 (a+1)X+a X+1  X (a+1)X aX+a+1 aX+1 aX (a+1)X (a+1)X+a  0 (a+1)X+a  a  a  0 X+1  1 (a+1)X
 0  0  0 (a+1)X  0  0  0 aX aX aX (a+1)X  X (a+1)X  X (a+1)X  X  X aX (a+1)X  X aX  0 (a+1)X  X aX aX  0  0  X aX  0  X  X aX (a+1)X (a+1)X (a+1)X  X aX (a+1)X (a+1)X aX aX  0 aX aX  0 aX (a+1)X  X  0 aX  0  0  0 (a+1)X
 0  0  0  0  X aX (a+1)X  X  0 aX  X (a+1)X aX  0 (a+1)X  X  X  0 aX  0  X (a+1)X (a+1)X aX  X aX aX aX  X  0 (a+1)X  X (a+1)X aX  0 (a+1)X  X aX  X  X  0 (a+1)X (a+1)X  X  0  0 aX  0  0  X  0 (a+1)X aX  X aX (a+1)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+372x^152+324x^153+660x^155+2412x^156+900x^157+1104x^159+5232x^160+1824x^161+2100x^163+6795x^164+2268x^165+2712x^167+9309x^168+2460x^169+2796x^171+9675x^172+2652x^173+2256x^175+5610x^176+1416x^177+588x^179+1317x^180+420x^181+72x^183+147x^184+24x^185+27x^188+18x^192+24x^196+12x^200+6x^204+3x^208

The gray image is a linear code over GF(4) with n=224, k=8 and d=152.
This code was found by Heurico 1.16 in 15.6 seconds.