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  1  1  1  1  1  1  1 X^2 X^2  1
 0 X^2+2  0 X^2  0  0 X^2 X^2+2 X^2+2 X^2+2  0  2  0  2 X^2+2 X^2+2  0 X^2 X^2  2  0 X^2+2  2 X^2+2 X^2 X^2  2  2  0 X^2 X^2  2 X^2+2 X^2+2  0  0 X^2  2  2  0 X^2 X^2  0  2 X^2  2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  2 X^2+2  2 X^2+2  0 X^2 X^2  0  0 X^2+2  2 X^2 X^2  2  0 X^2 X^2+2  2  2 X^2+2 X^2+2 X^2  0 X^2 X^2  2  2  2 X^2+2  0  0 X^2+2  0  0 X^2 X^2 X^2 X^2
 0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  0  2  0  0  2  2  2  2  0  0  2  2  0  0  0  0  0  0  2  2  0  2  2  2  0  2  2  2  0
 0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  2  0  2  0  2  2  0  2  2  0  2  0  0  0  0  0  0  2  2  0  0  0  2  2  2  2  0  0  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+56x^42+98x^44+192x^45+325x^46+192x^47+116x^48+34x^50+8x^52+1x^54+1x^88

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 0.078 seconds.