The generator matrix

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

generates a code of length 50 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+1482x^140+3216x^144+3696x^148+3576x^152+2712x^156+1425x^160+264x^164+6x^172+6x^176

The gray image is a linear code over GF(4) with n=200, k=7 and d=140.
This code was found by Heurico 1.16 in 24.5 seconds.