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  X  X X^2  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2 X+2  0 X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  0 X^2+X  2 X^2+X+2  2 X^2+X+2 X^2+X X^2+2 X^2+2  0
 0  0  2  0  0  0  2  2  2  0  0  0  2  2  2  2  2  2  2  0  2  0  0  0  0  2  0  0  2  2  0  2  2  2  2  2  0  0  2  2  0  0
 0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  0  2  0  0  2  2  2  0  2  0  0  2  2  0  0  2  2  2  2  2  2  2  0
 0  0  0  0  2  2  2  2  0  2  0  2  0  0  2  2  0  0  0  2  2  0  0  2  0  2  2  0  2  2  2  0  2  2  2  0  0  0  0  0  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+49x^38+28x^39+73x^40+148x^41+454x^42+116x^43+82x^44+12x^45+40x^46+16x^47+4x^48+1x^78

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 0.063 seconds.