The generator matrix

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

generates a code of length 40 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+120x^35+738x^36+1316x^37+2121x^38+2538x^39+2981x^40+2510x^41+1966x^42+1076x^43+696x^44+200x^45+46x^46+42x^47+20x^48+6x^49+2x^50+4x^52+1x^54

The gray image is a code over GF(2) with n=320, k=14 and d=140.
This code was found by Heurico 1.16 in 1.42 seconds.