The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+608x^34+2176x^35+5280x^36+9340x^37+14854x^38+21312x^39+23576x^40+21264x^41+15980x^42+9392x^43+4524x^44+1804x^45+648x^46+240x^47+53x^48+8x^49+4x^50+4x^52+2x^54+2x^56

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 75.1 seconds.