The generator matrix

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

generates a code of length 42 over F4[X]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+582x^116+648x^117+396x^118+1311x^120+1392x^121+840x^122+1641x^124+1596x^125+708x^126+1698x^128+1212x^129+684x^130+1455x^132+876x^133+384x^134+453x^136+420x^137+60x^138+15x^140+9x^144+3x^148

The gray image is a linear code over GF(4) with n=168, k=7 and d=116.
This code was found by Heurico 1.16 in 1.37 seconds.