The generator matrix

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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 149.

Homogenous weight enumerator: w(x)=1x^0+240x^149+540x^150+516x^151+1047x^152+2196x^153+2436x^154+2268x^155+3657x^156+4992x^157+5892x^158+3588x^159+6876x^160+10152x^161+9876x^162+7188x^163+12018x^164+15588x^165+16236x^166+9204x^167+15603x^168+19440x^169+17712x^170+9828x^171+15000x^172+16248x^173+14124x^174+7452x^175+8541x^176+8520x^177+5700x^178+2604x^179+2493x^180+2388x^181+1128x^182+360x^183+210x^184+108x^185+84x^186+36x^188+24x^192+9x^196+12x^200+3x^204+6x^208

The gray image is a linear code over GF(4) with n=224, k=9 and d=149.
This code was found by Heurico 1.16 in 212 seconds.