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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+50x^42+16x^43+94x^44+48x^45+626x^46+48x^47+83x^48+16x^49+22x^50+9x^52+6x^54+4x^56+1x^84

The gray image is a code over GF(2) with n=368, k=10 and d=168.
This code was found by Heurico 1.16 in 23.7 seconds.