The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+68x^34+640x^35+1863x^36+4762x^37+10044x^38+19026x^39+31144x^40+40540x^41+45214x^42+41494x^43+31425x^44+18908x^45+10029x^46+4400x^47+1595x^48+724x^49+172x^50+54x^51+18x^52+10x^53+9x^54+2x^55+2x^56

The gray image is a code over GF(2) with n=336, k=18 and d=136.
This code was found by Heurico 1.16 in 323 seconds.