The generator matrix

 1  0  0  1  1  1 X^2+X X^2+2  1  2  1  0  1  1  1  1  X  1 X+2  1  1 X^2+X  1  1  X  0  0  1  1  1  X X^2  1  1  1  1  0  1  1  1  1  1
 0  1  0  0  1 X+3  1  1 X^2+X  X X^2+X  1  3  3 X^2  2  1 X+3 X^2+X X^2 X^2+1  1 X+1 X^2+X+3  1 X^2+X+2  1  3 X^2+X+1 X^2+1  X  1 X^2+2  X X+1 X^2+2 X^2+X  1 X^2+2 X+1 X+1  0
 0  0  1  1  1 X^2+X  1  3  3  1 X^2+X X^2+X+2 X^2+3  2  X X^2+X+3 X^2+X+1 X+1  1 X^2+1 X^2+X X+2  1  1 X^2+3  1 X^2+X+2 X+1 X^2+X+3  X  1 X^2+X+3  2 X^2 X^2+2  0  1 X+2 X^2+X+2 X+1 X^2+X+1  0
 0  0  0  X  2 X+2 X+2 X^2+2 X^2 X+2 X^2+X X+2 X^2+X+2 X^2+2  2 X^2+X+2  X  0  X X^2  2 X^2+2 X^2+2 X^2+X+2  2  0 X^2+2 X^2+X+2 X^2+2 X+2  0  X  X X^2+X  2 X^2+X+2 X^2+X+2 X^2 X^2+2 X+2 X^2+2  0

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+94x^36+666x^37+1498x^38+2514x^39+3759x^40+4984x^41+5661x^42+5244x^43+4022x^44+2266x^45+1070x^46+602x^47+238x^48+84x^49+25x^50+24x^51+14x^52+2x^54

The gray image is a code over GF(2) with n=336, k=15 and d=144.
This code was found by Heurico 1.16 in 5.63 seconds.