The generator matrix

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

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+24x^96+48x^99+78x^100+288x^103+66x^104+432x^107+42x^108+21x^112+9x^116+15x^132

The gray image is a linear code over GF(4) with n=140, k=5 and d=96.
This code was found by Heurico 1.16 in 1.01e-007 seconds.