The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+236x^39+1336x^40+3310x^41+5008x^42+7770x^43+9406x^44+11328x^45+9768x^46+7752x^47+5015x^48+2922x^49+1084x^50+412x^51+114x^52+52x^53+8x^54+4x^55+4x^57+4x^58+2x^59

The gray image is a code over GF(2) with n=360, k=16 and d=156.
This code was found by Heurico 1.16 in 22.5 seconds.