The generator matrix

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

generates a code of length 50 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+165x^136+192x^137+384x^139+378x^140+612x^141+744x^143+582x^144+984x^145+1200x^147+948x^148+1536x^149+1920x^151+933x^152+1584x^153+1488x^155+726x^156+996x^157+408x^159+204x^160+216x^161+48x^164+24x^165+33x^168+27x^172+15x^176+30x^180+3x^184+3x^188

The gray image is a linear code over GF(4) with n=200, k=7 and d=136.
This code was found by Heurico 1.16 in 1.08 seconds.