The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+114x^38+124x^39+316x^40+200x^41+612x^42+216x^43+247x^44+72x^45+58x^46+28x^47+49x^48+8x^50+2x^52+1x^68

The gray image is a code over GF(2) with n=336, k=11 and d=152.
This code was found by Heurico 1.16 in 0.11 seconds.