The generator matrix

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

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+231x^112+1170x^116+2124x^120+4290x^124+4818x^128+3036x^132+555x^136+63x^140+45x^144+24x^148+15x^152+9x^156+3x^160

The gray image is a linear code over GF(4) with n=168, k=7 and d=112.
This code was found by Heurico 1.16 in 0.857 seconds.