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

generates a code of length 52 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+216x^137+300x^138+576x^139+843x^140+1620x^141+1908x^142+2856x^143+2886x^144+5028x^145+4704x^146+6432x^147+5631x^148+8724x^149+8376x^150+12192x^151+9195x^152+14772x^153+13968x^154+16836x^155+13479x^156+18216x^157+15156x^158+19416x^159+12288x^160+15612x^161+11616x^162+11640x^163+6966x^164+7908x^165+4608x^166+3456x^167+1716x^168+1524x^169+804x^170+324x^171+174x^172+108x^173+21x^176+21x^180+9x^184+6x^188+6x^192+6x^200

The gray image is a linear code over GF(4) with n=208, k=9 and d=137.
This code was found by Heurico 1.16 in 193 seconds.