The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  X  1  1  1  0  0  1  X  0  1  X  1  1  1  1  1  0  0  0  1  1  1
 0  X  0 X+2  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  0 X+2  X  2 X+2 X+2 X+2  0  0 X+2  X  X X+2 X+2  X X+2 X+2  0  X  0  2 X+2  X  X  X  X X+2 X+2
 0  0  2  0  0  0  0  0  0  0  2  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  2  0  2  0  2  2  2  0  0  0  0  2  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  0  2  2  2  0  2  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  2  2  0  2  0  0  2  2  2  2  2  0  2  2  0  0  0  2  0  2  0  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  0  0  2  2  2  0  0  2  0  2  0  2  2  0  0  0  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  0  0  2  0  2  0  2  2  2  0  2  0  0  2  2  2  0  0  2  0  2  0  0  0  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  0  2  2  2  0  2  0  2  2  2  2  0  2  2  0  2  2  2  2  2  2  2  2  2  2  2  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  0  0  0  2  0  0  2  0  0  2  0  2  2  2  0  0  0  2  0  2  0  2  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  0  2  0  2  2  2  2  0  2  0  0  0  2  2  0  2  2  2  0  2  0  0  2  0  0  0  0  0  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+122x^32+72x^34+16x^35+403x^36+176x^37+384x^38+656x^39+775x^40+1200x^41+624x^42+1200x^43+741x^44+656x^45+384x^46+176x^47+389x^48+16x^49+72x^50+101x^52+25x^56+3x^60

The gray image is a code over GF(2) with n=168, k=13 and d=64.
This code was found by Heurico 1.16 in 3.25 seconds.