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  1  1  1  1 X^2  1  0  1  1  1  X X^2  1  0  1  1 X^2  2 X^2  2
 0 X^2+2  0 X^2+2  2 X^2  2 X^2  0 X^2+2  0 X^2+2  2 X^2  2 X^2 X^2+2 X^2+2 X^2  0  2 X^2  0 X^2+2  2 X^2 X^2+2  0 X^2  2 X^2+2 X^2  0 X^2+2 X^2+2 X^2 X^2+2 X^2 X^2 X^2 X^2 X^2
 0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  0  2  2  0  2  2  2  0  0  0  2  2  2  2  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+14x^41+102x^42+6x^44+1x^48+2x^49+2x^54

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 0.078 seconds.