The generator matrix

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

generates a code of length 40 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+549x^34+2254x^35+5091x^36+9756x^37+14691x^38+21480x^39+22657x^40+22436x^41+15277x^42+9576x^43+4493x^44+1876x^45+665x^46+192x^47+42x^48+12x^49+18x^50+2x^51+4x^52

The gray image is a code over GF(2) with n=320, k=17 and d=136.
This code was found by Heurico 1.16 in 87 seconds.