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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+53x^38+97x^40+64x^41+621x^42+64x^43+74x^44+23x^46+18x^48+7x^50+1x^52+1x^76

The gray image is a code over GF(2) with n=336, k=10 and d=152.
This code was found by Heurico 1.16 in 2.22 seconds.