The generator matrix

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

generates a code of length 51 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+261x^144+336x^146+645x^148+384x^150+654x^152+288x^154+417x^156+384x^158+369x^160+144x^162+183x^164+18x^168+3x^172+9x^176

The gray image is a linear code over GF(4) with n=204, k=6 and d=144.
This code was found by Heurico 1.16 in 0.0827 seconds.