The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  X  X  X  2  X  2  X  0  X  0  X  2  X  2  1  1  1  1  X  2  X  1
 0  X  0 X+2  0 X+2  0  X  2 X+2  2  X  2 X+2  2  X X+2  X X+2  X  0  2  X  X  X  X X+2  X X+2  X  X  X  X  X  0  0  2  2  0  0  2  0
 0  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  0  0  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  2  0  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  2  0  2  2  2  0  0  2  2  0  0  2  0  2  2  0  0  2  2  0  0  0  0  0

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+10x^40+56x^41+9x^42+32x^43+4x^44+8x^45+4x^46+1x^48+2x^50+1x^58

The gray image is a code over GF(2) with n=168, k=7 and d=80.
This code was found by Heurico 1.16 in 0.0296 seconds.