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

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+27x^108+48x^111+78x^112+288x^115+57x^116+432x^119+54x^120+3x^124+18x^128+6x^132+9x^144+3x^148

The gray image is a linear code over GF(4) with n=156, k=5 and d=108.
This code was found by Heurico 1.16 in 0.016 seconds.