The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+148x^39+1002x^40+2906x^41+5524x^42+10100x^43+14828x^44+19442x^45+22607x^46+19908x^47+15527x^48+10262x^49+4942x^50+2444x^51+954x^52+278x^53+136x^54+40x^55+6x^56+8x^57+6x^58+2x^60+1x^62

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 88.2 seconds.