The generator matrix

 1  0  1  1  1  0  1  1  0  1  X  1  1  1  0  1  0  1  1  2 X+2  1  1  1 X+2  1  1  1  0  1  2  1  1  X  2  0  1  1  X  X
 0  1  1  0  1  1  2 X+1  1  0  1 X+1  1  2  1 X+3  1  X X+1  1  1 X+2  3 X+3  1  0  3 X+1  1 X+1  1  3  X  1  1  1 X+2 X+1 X+2  2
 0  0  X  0  0  0  0  0  0  0  0  2  2 X+2 X+2  X  X  X  X  X  2 X+2  X  0  X  0  2  X  X  2 X+2 X+2  0  2  X X+2  0  X  0  2
 0  0  0  X  0  0  0  0  X X+2 X+2 X+2 X+2 X+2  0  X X+2  2  2 X+2 X+2  X  X  2  0  2  X  2 X+2  X  2 X+2 X+2  2  2 X+2  0 X+2 X+2 X+2
 0  0  0  0  X  0  2 X+2  0  2  2  X X+2  X  X  2  X X+2  0  X  0 X+2  2 X+2  X  X  2 X+2  2  0  0  X  X X+2  0  0  X  2  0  0
 0  0  0  0  0  X X+2 X+2 X+2 X+2  0  0  X  0  0  X  X X+2  X  2 X+2 X+2  2  2  2  X  X  X  0 X+2  0  2 X+2  0  2 X+2  X  0  X  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+209x^32+80x^33+538x^34+348x^35+1243x^36+952x^37+1946x^38+1672x^39+2459x^40+1684x^41+1898x^42+1004x^43+1204x^44+352x^45+474x^46+48x^47+186x^48+4x^49+68x^50+9x^52+4x^54+1x^56

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 7.7 seconds.