The generator matrix

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

generates a code of length 53 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+261x^140+300x^141+300x^142+876x^143+2610x^144+2340x^145+1548x^146+2508x^147+6450x^148+5016x^149+3384x^150+5892x^151+12798x^152+9792x^153+5844x^154+9900x^155+19767x^156+14532x^157+8676x^158+14340x^159+25320x^160+16956x^161+8916x^162+12900x^163+22344x^164+12144x^165+6096x^166+6972x^167+10344x^168+5448x^169+1836x^170+1764x^171+2328x^172+1032x^173+264x^174+144x^175+87x^176+24x^177+48x^180+18x^184+18x^188+6x^200

The gray image is a linear code over GF(4) with n=212, k=9 and d=140.
This code was found by Heurico 1.16 in 197 seconds.