The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 (a+1)X  1  0  1  1  1 (a+1)X  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1  1  1  X  1  1  1  0  1  1  0  X  0  0
 0  1  0  0  0 (a+1)X  1 (a+1)X+a a+1 (a+1)X+1  1 (a+1)X+a  a (a+1)X+a+1  1 (a+1)X+a+1  1 (a+1)X+1 a+1  a  1  a  X (a+1)X  0 aX+1 a+1 (a+1)X+a  a aX+a+1  1 X+1  1 X+1 (a+1)X+a+1 (a+1)X+1 aX+1 (a+1)X+a X+a (a+1)X  1 aX  1 (a+1)X (a+1)X+a X+a+1  X a+1 aX+a+1  1  1  1 (a+1)X
 0  0  1  1  a a+1  1 X+1  1  0 a+1 X+a+1  a aX+a X+1 aX  a  a a+1  X X+a+1 X+a (a+1)X+a+1 aX (a+1)X+a  0 aX+1  X X+a+1 X+a+1  X (a+1)X+a (a+1)X+a (a+1)X+a  X aX+1 a+1 (a+1)X+1 aX a+1 aX+1  a aX+a+1 (a+1)X+1  a (a+1)X+a+1  1 aX+1  0  X (a+1)X+a (a+1)X+1  1
 0  0  0 (a+1)X  0  0  0 aX aX aX (a+1)X  X (a+1)X  X (a+1)X  X  X aX (a+1)X aX  X  X  X  X (a+1)X (a+1)X  0  0  X aX  0  0  0 aX  0  X aX  X (a+1)X  0 (a+1)X (a+1)X (a+1)X  0  0 aX  X aX  X  0 (a+1)X  X aX
 0  0  0  0  X aX (a+1)X  X  0 aX  X (a+1)X aX  0 (a+1)X  X  X  0 aX aX (a+1)X  X (a+1)X  0 aX  0  0 aX  0 aX aX aX  X  X  X  X  X  X  X (a+1)X  0  0 (a+1)X  0  X  X (a+1)X (a+1)X  0  X  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 144.

Homogenous weight enumerator: w(x)=1x^0+1107x^144+4764x^148+8715x^152+12732x^156+15690x^160+14277x^164+6783x^168+1320x^172+66x^176+24x^180+54x^184+3x^196

The gray image is a linear code over GF(4) with n=212, k=8 and d=144.
This code was found by Heurico 1.16 in 21 seconds.