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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+72x^112+204x^116+354x^120+1317x^124+1830x^128+72x^132+93x^136+57x^140+48x^144+18x^148+15x^152+12x^156+3x^160

The gray image is a linear code over GF(4) with n=168, k=6 and d=112.
This code was found by Heurico 1.16 in 0.12 seconds.