The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+516x^42+688x^43+782x^44+686x^45+397x^46+390x^47+307x^48+110x^49+142x^50+42x^51+30x^52+4x^53+1x^54

The gray image is a code over GF(2) with n=360, k=12 and d=168.
This code was found by Heurico 1.16 in 0.125 seconds.