The generator matrix

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

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+204x^35+430x^36+746x^37+1103x^38+1400x^39+1675x^40+1766x^41+1776x^42+1798x^43+1760x^44+1356x^45+1014x^46+646x^47+352x^48+238x^49+69x^50+30x^51+4x^52+6x^53+5x^54+2x^55+2x^56+1x^58

The gray image is a code over GF(2) with n=168, k=14 and d=70.
This code was found by Heurico 1.13 in 2.54 seconds.