The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+33x^36+44x^37+47x^38+172x^39+99x^40+442x^41+424x^42+432x^43+99x^44+134x^45+26x^46+36x^47+18x^48+14x^49+11x^50+4x^52+6x^53+3x^54+2x^56+1x^66

The gray image is a code over GF(2) with n=336, k=11 and d=144.
This code was found by Heurico 1.16 in 0.109 seconds.