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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+54x^104+282x^108+372x^112+48x^114+438x^116+576x^118+441x^120+2592x^122+465x^124+5184x^126+498x^128+3888x^130+477x^132+375x^136+345x^140+189x^144+105x^148+54x^152

The gray image is a linear code over GF(4) with n=168, k=7 and d=104.
This code was found by Heurico 1.16 in 1.66 seconds.