The generator matrix

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

generates a code of length 55 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+150x^148+180x^149+132x^150+180x^151+1275x^152+1080x^153+972x^154+576x^155+2889x^156+2124x^157+1692x^158+1032x^159+4899x^160+3324x^161+2556x^162+1164x^163+5997x^164+4272x^165+2508x^166+1332x^167+6993x^168+4272x^169+2772x^170+1224x^171+4569x^172+2364x^173+1428x^174+528x^175+1620x^176+732x^177+228x^178+108x^179+180x^180+84x^181+45x^184+30x^188+12x^192+6x^196+3x^200+3x^212

The gray image is a linear code over GF(4) with n=220, k=8 and d=148.
This code was found by Heurico 1.16 in 15.3 seconds.