The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X  1  1  1  1  X  1  1  1  1  1  1  1  1  X  1  1  1  1  1  X  1  X  X  X
 0  X  0 X+2  2 3X+2 2X+2  X  2 X+2  0 X+2 2X 3X  2  X X+2  X  0 X+2 2X+2 3X 2X 3X+2 2X+2  X  0  2  0 3X+2 3X+2 3X+2 2X+2  X  0 2X  2  X  X X+2 2X+2 X+2
 0  0 2X+2  0  2  2 2X  2  2  0 2X 2X+2  2  2 2X 2X  0 2X+2  0  0 2X 2X 2X+2  2 2X  2 2X  0  2  0 2X  2 2X+2  0  2 2X+2  0  2 2X+2  0 2X+2 2X
 0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0  0  0  0 2X  0  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X  0  0  0 2X 2X  0 2X 2X 2X 2X  0 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+163x^38+44x^39+253x^40+352x^41+514x^42+328x^43+196x^44+32x^45+79x^46+12x^47+60x^48+12x^50+1x^52+1x^68

The gray image is a code over GF(2) with n=336, k=11 and d=152.
This code was found by Heurico 1.16 in 0.172 seconds.