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

generates a code of length 43 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+12x^42+96x^43+12x^44+2x^46+3x^48+2x^54

The gray image is a code over GF(2) with n=344, k=7 and d=168.
This code was found by Heurico 1.16 in 0.047 seconds.