The generator matrix

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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+28x^41+84x^42+6x^44+4x^46+4x^49+1x^56

The gray image is a code over GF(2) with n=336, k=7 and d=164.
This code was found by Heurico 1.16 in 0.031 seconds.