The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+240x^39+142x^40+216x^41+32x^42+132x^43+44x^44+88x^45+64x^47+33x^48+16x^49+12x^51+4x^52

The gray image is a code over GF(2) with n=168, k=10 and d=78.
This code was found by Heurico 1.16 in 40.6 seconds.