The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+216x^40+734x^41+1574x^42+1942x^43+2538x^44+2698x^45+2445x^46+1920x^47+1310x^48+480x^49+292x^50+132x^51+58x^52+22x^53+9x^54+4x^55+3x^56+2x^57+2x^59+2x^60

The gray image is a code over GF(2) with n=360, k=14 and d=160.
This code was found by Heurico 1.16 in 1.81 seconds.