The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  2  1  1  X  X  1  2  1  1  1  0  X  1  1  X  1  1 X+2  1  2 X+2  1 X+2  0 X+2  0 X+2 X+2  1  1  1
 0  1  0  0  1  1  1  X  2  3  1  1  2  3  0 X+2  1  1  2  X  1  1  2 X+2 X+3  1  2 X+1  1  X  1 X+2 X+3  1 X+2  1  1  1  1  X X+1  0
 0  0  1  1  2  3  1  1  X X+2  X X+3 X+1 X+3  1  1  X  1  3 X+2 X+1  2  1  0  0 X+3  2 X+2  3  3  X  1 X+1 X+2  1 X+3 X+1  1  X  0  0  1
 0  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  2  2  2  0  0  0  2  2  0  2  0  2  2  0  0

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+21x^38+190x^39+160x^40+204x^41+95x^42+108x^43+40x^44+60x^45+28x^46+34x^47+31x^48+40x^49+7x^50+4x^51+1x^54

The gray image is a code over GF(2) with n=168, k=10 and d=76.
This code was found by Heurico 1.11 in 0.0335 seconds.