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

generates a code of length 52 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+303x^140+132x^141+360x^142+360x^143+1644x^144+804x^145+1044x^146+1392x^147+3474x^148+1788x^149+1932x^150+1860x^151+5223x^152+2292x^153+2544x^154+2784x^155+6345x^156+3228x^157+2832x^158+3408x^159+6618x^160+2604x^161+2436x^162+2064x^163+3894x^164+1188x^165+1020x^166+420x^167+924x^168+252x^169+120x^170+159x^172+30x^176+24x^180+21x^184+9x^188+3x^192

The gray image is a linear code over GF(4) with n=208, k=8 and d=140.
This code was found by Heurico 1.16 in 14.4 seconds.