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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+52x^40+96x^42+32x^43+81x^44+480x^45+584x^46+480x^47+69x^48+32x^49+80x^50+45x^52+8x^54+6x^56+1x^60+1x^84

The gray image is a code over GF(2) with n=368, k=11 and d=160.
This code was found by Heurico 1.16 in 0.141 seconds.