The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+202x^36+404x^37+680x^38+724x^39+899x^40+852x^41+904x^42+784x^43+847x^44+644x^45+522x^46+348x^47+222x^48+84x^49+52x^50+19x^52+2x^54+2x^56

The gray image is a code over GF(2) with n=168, k=13 and d=72.
This code was found by Heurico 1.13 in 0.687 seconds.