The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+339x^34+1566x^35+4609x^36+9344x^37+19067x^38+28978x^39+44583x^40+44896x^41+44347x^42+29656x^43+19873x^44+8932x^45+3813x^46+1412x^47+528x^48+120x^49+50x^50+18x^51+6x^52+4x^53+2x^55

The gray image is a code over GF(2) with n=328, k=18 and d=136.
This code was found by Heurico 1.16 in 326 seconds.