The generator matrix

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

generates a code of length 35 over F4[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+60x^84+264x^88+396x^92+192x^94+474x^96+1152x^98+465x^100+3072x^102+501x^104+4992x^106+492x^108+2880x^110+495x^112+492x^116+291x^120+108x^124+54x^128+3x^132

The gray image is a linear code over GF(4) with n=140, k=7 and d=84.
This code was found by Heurico 1.16 in 1.31 seconds.