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

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+456x^136+924x^137+480x^138+900x^139+2202x^140+2052x^141+1416x^142+1884x^143+4008x^144+2808x^145+1848x^146+2364x^147+4890x^148+4020x^149+2760x^150+2880x^151+5685x^152+4308x^153+2616x^154+2868x^155+4602x^156+3108x^157+1392x^158+1284x^159+1929x^160+1080x^161+240x^162+108x^163+282x^164+132x^165+9x^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 12.2 seconds.