The generator matrix

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

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+30x^34+30x^35+52x^36+50x^37+109x^38+438x^39+672x^40+434x^41+90x^42+42x^43+30x^44+22x^45+18x^46+2x^47+7x^48+6x^49+8x^50+6x^52+1x^70

The gray image is a code over GF(2) with n=320, k=11 and d=136.
This code was found by Heurico 1.16 in 0.109 seconds.