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

generates a code of length 43 over F4[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+99x^108+321x^112+348x^116+507x^120+768x^123+390x^124+4608x^127+552x^128+6912x^131+468x^132+405x^136+396x^140+330x^144+201x^148+60x^152+15x^156+3x^164

The gray image is a linear code over GF(4) with n=172, k=7 and d=108.
This code was found by Heurico 1.16 in 1.73 seconds.