The generator matrix

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

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+81x^32+154x^33+220x^34+284x^35+464x^36+670x^37+876x^38+1258x^39+1483x^40+1684x^41+1872x^42+1824x^43+1596x^44+1236x^45+904x^46+628x^47+398x^48+322x^49+196x^50+100x^51+68x^52+30x^53+28x^54+2x^55+4x^56+1x^72

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 10.7 seconds.