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

generates a code of length 39 over F4[X]/(X^2) who�s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+258x^108+1080x^112+963x^116+1071x^120+636x^124+69x^128+3x^132+3x^136+12x^140

The gray image is a linear code over GF(4) with n=156, k=6 and d=108.
This code was found by Heurico 1.16 in 0.0564 seconds.