The generator matrix

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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+70x^39+1165x^40+2720x^41+5681x^42+9806x^43+15341x^44+19218x^45+22655x^46+19836x^47+15572x^48+9816x^49+5473x^50+2216x^51+1055x^52+268x^53+109x^54+38x^55+18x^56+8x^57+2x^58+2x^59+2x^61

The gray image is a code over GF(2) with n=368, k=17 and d=156.
This code was found by Heurico 1.16 in 92.5 seconds.