The generator matrix

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

generates a code of length 49 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+429x^136+372x^137+324x^138+276x^139+1158x^140+864x^141+708x^142+372x^143+1830x^144+1188x^145+744x^146+348x^147+1503x^148+972x^149+648x^150+252x^151+1152x^152+744x^153+468x^154+192x^155+804x^156+420x^157+180x^158+96x^159+273x^160+48x^161+3x^164+3x^168+12x^172

The gray image is a linear code over GF(4) with n=196, k=7 and d=136.
This code was found by Heurico 1.16 in 0.842 seconds.