The generator matrix

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

generates a code of length 35 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 98.

Homogenous weight enumerator: w(x)=1x^0+288x^98+336x^99+60x^100+912x^102+636x^103+117x^104+456x^106+108x^107+24x^108+384x^110+372x^111+39x^112+264x^114+84x^115+12x^116+3x^120

The gray image is a linear code over GF(4) with n=140, k=6 and d=98.
This code was found by Heurico 1.16 in 0.0516 seconds.