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

generates a code of length 43 over F4[X]/(X^2) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+120x^126+45x^128+72x^134+15x^136+3x^152

The gray image is a linear code over GF(4) with n=172, k=4 and d=126.
This code was found by Heurico 1.16 in -1.01e-007 seconds.