The generator matrix

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

generates a code of length 35 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+9x^100+144x^101+288x^102+27x^104+96x^105+216x^106+21x^108+144x^109+72x^114+6x^124

The gray image is a linear code over GF(4) with n=140, k=5 and d=100.
This code was found by Heurico 1.16 in 3.24e-008 seconds.