The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+15x^34+41x^36+60x^38+128x^39+569x^40+128x^41+38x^42+18x^44+8x^46+4x^48+3x^50+5x^52+4x^54+1x^56+1x^64

The gray image is a code over GF(2) with n=320, k=10 and d=136.
This code was found by Heurico 1.16 in 0.047 seconds.