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

generates a code of length 42 over Z4[X]/(X^2+2) 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.