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  X  1  1  1  X
 0 2X+2  0  0 2X 2X+2 2X+2  2  0 2X  0  2 2X+2 2X 2X+2 2X+2  0  2  2  0  2 2X  2  0  2  0 2X  2  0 2X+2 2X  2 2X  0 2X 2X+2 2X+2 2X  2 2X+2 2X 2X
 0  0 2X+2  0 2X+2 2X+2  2 2X  0  2  2 2X+2 2X+2 2X  0  0 2X 2X+2  2 2X+2  0  2  0 2X 2X+2  2 2X 2X  0 2X+2 2X+2  0  2 2X+2  0 2X  2  0 2X+2 2X 2X+2  2
 0  0  0 2X+2  2 2X  2  2 2X 2X  2 2X 2X+2  2 2X+2 2X 2X  2 2X  2 2X  0  2 2X+2 2X+2 2X  0 2X+2  2  0 2X+2 2X+2  2 2X  0  2 2X  2  0 2X 2X 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+48x^38+72x^40+64x^41+664x^42+64x^43+60x^44+40x^46+10x^48+1x^80

The gray image is a code over GF(2) with n=336, k=10 and d=152.
This code was found by Heurico 1.16 in 0.062 seconds.