The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^40+80x^41+136x^42+128x^43+446x^44+288x^45+612x^46+64x^47+99x^48+80x^49+48x^50+9x^52+4x^54+1x^84

The gray image is a code over GF(2) with n=360, k=11 and d=160.
This code was found by Heurico 1.16 in 0.125 seconds.