The generator matrix

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

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+73x^38+178x^39+235x^40+472x^41+205x^42+452x^43+140x^44+168x^45+100x^46+10x^47+4x^48+5x^50+2x^52+1x^54+2x^56

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 0.063 seconds.