The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+56x^32+170x^33+375x^34+690x^35+1057x^36+1272x^37+1604x^38+2024x^39+1962x^40+1860x^41+1758x^42+1394x^43+932x^44+568x^45+348x^46+174x^47+84x^48+34x^49+11x^50+4x^51+3x^52+2x^55+1x^64

The gray image is a code over GF(2) with n=160, k=14 and d=64.
This code was found by Heurico 1.16 in 6.59 seconds.