The generator matrix

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

generates a code of length 34 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 98.

Homogenous weight enumerator: w(x)=1x^0+288x^98+180x^100+264x^102+9x^104+144x^106+60x^108+72x^110+3x^112+3x^120

The gray image is a linear code over GF(4) with n=136, k=5 and d=98.
This code was found by Heurico 1.16 in 0.188 seconds.