The generator matrix

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

generates a code of length 35 over F4[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+120x^96+132x^97+168x^98+468x^100+372x^101+192x^102+384x^104+492x^105+144x^106+531x^108+444x^109+192x^110+252x^112+96x^113+72x^114+18x^116+15x^124+3x^128

The gray image is a linear code over GF(4) with n=140, k=6 and d=96.
This code was found by Heurico 1.16 in 0.0481 seconds.