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 X 1 1 1 1 1 1 1 2X 1 1 1 1 X X X
0 2X+2 0 2X+2 0 2X+2 0 2 2X 2X+2 0 2X+2 2X+2 0 2X 2 0 2 2X 2X+2 2 2 2X+2 0 0 2X 2X 2X+2 2X+2 2X+2 2X+2 0 2 0 0 2X+2 2X 2X 0 2X 0 2X 2X+2 0 2X
0 0 2X 0 0 0 0 0 2X 0 0 2X 2X 2X 2X 0 0 2X 0 0 2X 2X 0 0 2X 2X 2X 0 2X 2X 2X 0 2X 0 2X 0 0 0 0 2X 2X 0 2X 0 0
0 0 0 2X 0 0 0 2X 0 0 0 2X 0 0 0 2X 2X 0 2X 2X 0 2X 0 2X 2X 0 2X 0 2X 2X 0 0 2X 2X 2X 0 2X 0 0 2X 0 2X 2X 0 0
0 0 0 0 2X 0 0 0 0 2X 2X 0 2X 0 2X 2X 2X 0 0 2X 0 0 2X 0 2X 2X 2X 0 2X 0 2X 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0
0 0 0 0 0 2X 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 2X 0 2X 2X 0 0 0 0 0 2X 0 2X 2X 0 2X 2X 2X
0 0 0 0 0 0 2X 0 2X 0 2X 0 0 0 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 2X 2X 2X 0 0 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+153x^40+978x^44+640x^46+212x^48+54x^52+9x^56+1x^80
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 43.7 seconds.