The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+348x^98+336x^99+90x^100+780x^102+552x^103+75x^104+504x^106+288x^107+24x^108+444x^110+264x^111+51x^112+228x^114+96x^115+6x^116+9x^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 0.032 seconds.