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  1  1  1  1  1  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 a+1 aX  1 (a+1)X  0 X+a+1  a aX+1 (a+1)X+a+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 X+a  X aX+1 (a+1)X+1  a a+1  0 aX+a X+a
 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 aX  0  0 (a+1)X aX aX 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+324x^145+672x^146+348x^147+69x^148+1356x^149+1284x^150+444x^151+63x^152+1524x^153+1596x^154+564x^155+42x^156+1476x^157+1500x^158+420x^159+18x^160+1224x^161+1116x^162+336x^163+15x^164+768x^165+624x^166+144x^167+24x^168+240x^169+120x^170+48x^171+12x^172+3x^176+6x^180+3x^184

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 5.4 seconds.