The generator matrix

 1  0  0  1  1  1  0 X^2+2 X^2+2 X^2  1  1  1  1  1  1 X^2+X+2  X X+2  1  1 X+2 X^2+X  2  1  1  1  1  1  1  1  1 X^2+X  1 X^2+2  1  1 X^2+X  1 X^2 X^2  1
 0  1  0  0 X^2+3 X^2+1  1  X  1  1 X^2+X X^2+X+3 X+3 X+2 X+1 X^2+3  1 X^2+X+2  1  2 X^2  1  1  1  1 X^2+X X^2+X+1 X+1 X^2+X+2 X^2+X X^2+1  X  1  1  1 X^2+2 X+2  1  2  1  1 X^2+2
 0  0  1 X+1 X+1  0 X^2+X+1  1  X  1 X^2+1 X+2 X^2+X+1 X^2 X^2+1 X^2+X X+2  1 X+3 X+2 X^2+3 X^2+3  2 X^2+2  X  X  X X^2+1 X+1 X^2+X+1 X^2+2  X X+2  3 X+3  0  0 X^2 X^2+X+1  1 X^2  0
 0  0  0 X^2 X^2+2  2 X^2 X^2+2 X^2  0  2 X^2  2 X^2 X^2+2  0  2  0  2  0 X^2+2 X^2 X^2+2  2 X^2+2 X^2  2  0  2 X^2+2  0  0 X^2 X^2+2  0 X^2  2  0  2 X^2+2 X^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+162x^37+692x^38+1492x^39+2218x^40+2244x^41+2920x^42+2422x^43+2018x^44+1214x^45+622x^46+228x^47+70x^48+44x^49+28x^50+2x^51+4x^52+2x^54+1x^56

The gray image is a code over GF(2) with n=336, k=14 and d=148.
This code was found by Heurico 1.16 in 1.5 seconds.