The generator matrix

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

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+606x^136+828x^137+432x^138+1020x^139+2226x^140+1692x^141+1212x^142+2100x^143+4134x^144+2724x^145+1740x^146+2628x^147+5337x^148+3888x^149+2232x^150+3372x^151+5940x^152+3744x^153+2100x^154+3144x^155+5124x^156+3096x^157+1176x^158+1392x^159+1881x^160+816x^161+288x^162+168x^163+345x^164+108x^165+36x^166+6x^168

The gray image is a linear code over GF(4) with n=200, k=8 and d=136.
This code was found by Heurico 1.16 in 14.5 seconds.