The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  2  2  0  0  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  X  X X+2  X  X X+2 X+2  X  X X+2 X+2  2  X  X X+2  X  0  X  2  X  2
 0  0  X  0  0  0  0  0  0  0  X X+2  X X+2 X+2  X X+2  0  2  2  2  2  X  X  0  2  X  2  0  X  X  0 X+2  X  2 X+2  0  2  X  0 X+2  0
 0  0  0  X  0  0  0  X X+2  X  X  X  0 X+2  0 X+2  2  X  0  2  2  X X+2  2  X X+2  0 X+2  0  2  0  2  2  X  0  2  0  0  0  X  0  0
 0  0  0  0  X  0  X  X  X  2  0  0  2 X+2  X X+2  X  X X+2  X  2 X+2  X X+2  X  X  X  2 X+2 X+2  0  0 X+2  0 X+2  0  0  X X+2  X  2  0
 0  0  0  0  0  X  X  2 X+2 X+2  0  X  X  X  0  2  X  0 X+2  0  X  X  2  0  0  X X+2  2  2 X+2  0 X+2 X+2 X+2  X  2  0  X X+2 X+2 X+2  X
 0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  0  0  2  2  0  2  2  2  0  0  2  2  2  2  2  2  2  2  0  2  0  0  2  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+85x^32+114x^33+204x^34+284x^35+376x^36+492x^37+658x^38+998x^39+1573x^40+2206x^41+2350x^42+2234x^43+1654x^44+978x^45+656x^46+494x^47+338x^48+280x^49+214x^50+82x^51+66x^52+26x^53+13x^54+4x^55+3x^56+1x^70

The gray image is a code over GF(2) with n=168, k=14 and d=64.
This code was found by Heurico 1.16 in 10.9 seconds.