The generator matrix

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

generates a code of length 50 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+1164x^144+1308x^148+624x^152+504x^156+381x^160+108x^164+6x^176

The gray image is a linear code over GF(4) with n=200, k=6 and d=144.
This code was found by Heurico 1.16 in 3.01 seconds.