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  1  0  1  1  X  1  1  1  1  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 X+a  1  0  1  1 a*X+1 a^2 a*X+a^2  a a^2*X
 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  0  a a*X+1  a a^2 X+a^2 X+a^2 a^2*X+a a^2*X+1  0
 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 a^2*X a^2*X a*X  0  0 a^2*X  0  X  X a*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+1077x^116+3204x^120+4080x^124+3975x^128+2586x^132+1428x^136+24x^140+9x^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 15.3 seconds.