The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+94x^32+410x^33+949x^34+1940x^35+3180x^36+5130x^37+7601x^38+10112x^39+12927x^40+15080x^41+15602x^42+15212x^43+13549x^44+10394x^45+7709x^46+5096x^47+2950x^48+1612x^49+756x^50+456x^51+195x^52+76x^53+22x^54+16x^55+2x^57+1x^58

The gray image is a code over GF(2) with n=168, k=17 and d=64.
This code was found by Heurico 1.13 in 121 seconds.