The generator matrix

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

generates a code of length 52 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+432x^145+720x^146+216x^147+57x^148+1284x^149+1296x^150+540x^151+63x^152+1452x^153+1596x^154+576x^155+51x^156+1380x^157+1368x^158+504x^159+33x^160+1332x^161+1152x^162+360x^163+12x^164+840x^165+600x^166+108x^167+15x^168+192x^169+180x^170+15x^172+9x^180

The gray image is a linear code over GF(4) with n=208, k=7 and d=145.
This code was found by Heurico 1.16 in 2.48 seconds.