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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+141x^120+360x^124+462x^128+24x^132+18x^136+6x^144+9x^152+3x^160

The gray image is a linear code over GF(4) with n=168, k=5 and d=120.
This code was found by Heurico 1.16 in 0.016 seconds.