The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+9x^38+16x^40+32x^41+399x^42+32x^43+12x^44+7x^46+3x^48+1x^82

The gray image is a code over GF(2) with n=336, k=9 and d=152.
This code was found by Heurico 1.16 in 0.031 seconds.