The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  2  1 X+2  1  1  1  0  1  1  1  1 X+2  1  1  1  1  1  2  1  1 X+2  X  1  1  0  X  0  1
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  1  0  1  3 X+1  2  1 X+2 X+1  X  3  1 X+2  X X+2 X+1  0  1  1  X  1  1 X+1  X  X  X  1  3
 0  0  X  0  0  0  0  0  0  2  2 X+2  X  X  X  2 X+2  X  X X+2  0 X+2 X+2  0  2 X+2  0  2  2  X  2  X  0  0  X  2  0  X X+2 X+2
 0  0  0  X  0  0  X  2  X  2 X+2  2 X+2  2  0 X+2  X  X  2  2  X  X  X  2  2  X  X  2  0  2  X X+2 X+2  2  X X+2  X  0  2 X+2
 0  0  0  0  X  0  0 X+2  2  0  2  2 X+2  X  X  X  0 X+2 X+2 X+2 X+2 X+2  2  0  0 X+2 X+2  2 X+2  2  0  0 X+2  X  X  X  2  2  0  2
 0  0  0  0  0  2  0  0  2  0  2  0  2  0  2  0  0  0  0  2  2  2  2  2  2  2  0  0  0  2  2  0  0  2  2  0  0  2  0  2
 0  0  0  0  0  0  2  2  0  2  2  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  2  2  2  0  0  2  2  0  0  0  0  2  0  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+207x^32+48x^33+558x^34+404x^35+1217x^36+940x^37+1982x^38+1732x^39+2378x^40+1500x^41+1966x^42+1148x^43+1170x^44+324x^45+498x^46+44x^47+196x^48+4x^49+52x^50+13x^52+2x^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 8.5 seconds.