The generator matrix

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

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+66x^140+24x^141+204x^143+303x^144+348x^145+588x^147+525x^148+672x^149+1056x^151+765x^152+1368x^153+1416x^155+831x^156+1848x^157+1596x^159+798x^160+1452x^161+1068x^163+549x^164+432x^165+216x^167+126x^168+39x^172+24x^176+33x^180+15x^184+18x^188+3x^196

The gray image is a linear code over GF(4) with n=208, k=7 and d=140.
This code was found by Heurico 1.16 in 1.12 seconds.