The generator matrix

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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+50x^37+106x^38+158x^39+160x^40+320x^41+518x^42+320x^43+150x^44+126x^45+60x^46+22x^47+7x^48+12x^49+17x^50+12x^51+2x^52+4x^53+2x^54+1x^66

The gray image is a code over GF(2) with n=336, k=11 and d=148.
This code was found by Heurico 1.16 in 31.6 seconds.