The generator matrix

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

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+163x^38+44x^39+253x^40+352x^41+514x^42+328x^43+196x^44+32x^45+79x^46+12x^47+60x^48+12x^50+1x^52+1x^68

The gray image is a code over GF(2) with n=336, k=11 and d=152.
This code was found by Heurico 1.16 in 0.172 seconds.