The generator matrix

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

generates a code of length 52 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 149.

Homogenous weight enumerator: w(x)=1x^0+336x^149+684x^150+96x^152+540x^153+660x^154+90x^156+216x^157+396x^158+39x^160+144x^161+324x^162+216x^165+168x^166+24x^168+84x^169+72x^170+6x^172

The gray image is a linear code over GF(4) with n=208, k=6 and d=149.
This code was found by Heurico 1.16 in 0.062 seconds.