The generator matrix

 1  0  0  1  1  1  X  1  1  0  1  2  X  1  1  1 X^2+X  0 X^2+X+2  1  1 X^2+2  1 X^2+X+2 X^2+2  1  1  1  1  1  1  2 X^2  1  1  1  1  1  X  2
 0  1  0  0 X^2+1 X+3  1 X^2+X+3 X^2+X X^2 X+3  1  1 X^2 X^2+X+2 X^2+3  X  1  1 X^2+X+1 X^2+1  1 X^2+X+2  2  1  0 X^2+X X^2+X+1 X^2+X+2 X^2+3 X+1  X  1  2 X^2+X+1 X^2+2  3 X^2+X+2  X  X
 0  0  1  1  1 X^2 X^2+1 X+3  3  1 X+2 X^2+2  3 X^2+X+2  3 X^2  1 X^2+3 X^2+2 X^2+X+3 X^2+X+2 X^2+X+1 X^2+X+1  1  X X^2+1  X X^2+1 X^2+2  1  1  1  X X+1 X+1 X+1 X+3  0 X^2  1
 0  0  0  X X+2  2 X+2 X^2+X+2  X  X X^2 X+2 X^2 X^2+X X^2+2 X^2+X+2 X^2+X X^2 X^2  0  2  0 X^2+X  2 X^2+X+2 X^2+2  2 X^2+X+2  0 X^2+X  0 X^2  2  X X^2  0 X^2+X  X X^2+X+2 X^2+X+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+506x^35+1457x^36+2710x^37+3680x^38+5294x^39+5442x^40+5744x^41+3655x^42+2258x^43+1209x^44+542x^45+150x^46+82x^47+19x^48+12x^49+3x^50+4x^51

The gray image is a code over GF(2) with n=320, k=15 and d=140.
This code was found by Heurico 1.16 in 562 seconds.