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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+9x^40+30x^41+198x^42+6x^44+9x^46+1x^54+2x^57

The gray image is a code over GF(2) with n=336, k=8 and d=160.
This code was found by Heurico 1.16 in 0.031 seconds.