The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+314x^39+463x^40+948x^41+877x^42+1592x^43+1104x^44+2246x^45+1298x^46+2302x^47+1138x^48+1658x^49+808x^50+870x^51+342x^52+250x^53+86x^54+40x^55+21x^56+18x^57+3x^58+2x^59+2x^60+1x^64

The gray image is a code over GF(2) with n=184, k=14 and d=78.
This code was found by Heurico 1.16 in 59.7 seconds.