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  1  1  1  1  1  X  1  1 X^2  1  X  1  X X^2
 0 X^2+2  0 X^2  0  0 X^2 X^2  2  2 X^2 X^2+2 X^2+2 X^2+2  0  2  0 X^2  2 X^2 X^2+2  0  0 X^2 X^2 X^2  0  2  2  0 X^2 X^2+2  0  0  2  0 X^2  2  2 X^2  2  0  0 X^2+2 X^2+2
 0  0 X^2+2 X^2  0 X^2+2 X^2+2  0  2 X^2 X^2  0  2 X^2  2 X^2+2  0 X^2+2 X^2+2  2  0 X^2  0 X^2  2  2  0  0 X^2 X^2 X^2 X^2  0  2  0  0 X^2  2  0 X^2+2 X^2 X^2+2  2  0  2
 0  0  0  2  0  0  2  0  0  0  0  2  2  0  2  2  2  2  2  2  0  2  2  0  0  2  0  2  2  0  2  0  0  0  0  2  0  0  2  0  2  0  2  2  2
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  2  2  0  2  0  0  2  2  2  2  2  2  2  0  0  2  2  0  0  0  0  2  2  2  2  0  2  2  2  2  0
 0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  0  0  2  2  0  2  2  2  0  0  0  2  2  0  0  0  0  2  2  2  0  2  2  2  0  0  0  2  0  2

generates a code of length 45 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+121x^40+102x^42+128x^43+430x^44+512x^45+410x^46+128x^47+116x^48+58x^50+34x^52+6x^54+1x^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 0.141 seconds.