The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+122x^36+236x^38+80x^39+324x^40+192x^41+266x^42+160x^43+286x^44+64x^45+120x^46+16x^47+110x^48+42x^50+20x^52+8x^54+1x^64

The gray image is a code over GF(2) with n=168, k=11 and d=72.
This code was found by Heurico 1.16 in 0.194 seconds.