The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+66x^35+220x^36+352x^37+602x^38+656x^39+932x^40+732x^41+1115x^42+764x^43+982x^44+608x^45+533x^46+292x^47+158x^48+92x^49+47x^50+10x^51+9x^52+8x^53+5x^54+4x^55+1x^56+2x^58+1x^60

The gray image is a code over GF(2) with n=168, k=13 and d=70.
This code was found by Heurico 1.16 in 1.76 seconds.