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^2*X+a^2  0 a^2*X+1 a^2*X+a^2  X  a  1 a^2*X+1 X+a a*X+a^2  1  X  1 X+a a*X+a^2  1  0  X a*X a*X a^2*X+1 a*X+1 a*X+1 a*X+1 a*X  1  a X+a a*X+a a*X+a a*X+a
 0  0 a^2*X a*X  X  X  0 a^2*X a*X a^2*X a^2*X  X  0 a*X a*X a^2*X a*X  X  0  X a*X  X  0 a^2*X a*X a^2*X  X  0  X  X  0 a^2*X a*X  X  0

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

Homogenous weight enumerator: w(x)=1x^0+9x^100+144x^101+300x^102+27x^104+96x^105+180x^106+21x^108+144x^109+36x^110+60x^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 -3.62e-008 seconds.