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

generates a code of length 35 over F4[X]/(X^2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+105x^92+171x^96+192x^99+195x^100+1152x^103+153x^104+1728x^107+108x^108+84x^112+75x^116+69x^120+33x^124+18x^128+12x^132

The gray image is a linear code over GF(4) with n=140, k=6 and d=92.
This code was found by Heurico 1.16 in 0.0943 seconds.