The generator matrix

 1  0  1  1  2  1  1  1 X+2  1  1  X  1  0  1 3X  1 3X  1  1 X+2  1  2  1  2  1  1  1  1  1  1 3X+2  1  1  1 3X+2  X  1  1  0  1  1
 0  1  1 X+2  1 X+3  2  3  1 3X 3X+1  1  3  1 3X+2  1 2X+2  1 X+1 2X+1  1 X+3  1 2X+1  1 X+1 3X+2  1 X+1 X+2 2X+1  1 2X+1 3X+1  2  1  0 3X+1 X+2  1  0  0
 0  0  X  0 3X  X 3X 2X  0 3X+2 2X+2  X 2X+2 2X+2 3X  2 X+2 X+2 2X 2X 2X+2 X+2 2X+2 3X+2  X  X  2  2  0 3X+2 3X+2 X+2 3X 3X+2 2X+2  0 X+2 3X+2 2X+2 3X+2 3X+2 2X
 0  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  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+133x^38+342x^39+754x^40+544x^41+689x^42+528x^43+620x^44+272x^45+127x^46+34x^47+24x^48+8x^49+10x^50+8x^52+1x^56+1x^58

The gray image is a code over GF(2) with n=336, k=12 and d=152.
This code was found by Heurico 1.16 in 0.172 seconds.