The generator matrix

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

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+135x^32+144x^33+415x^34+580x^35+1003x^36+1372x^37+1570x^38+1988x^39+1968x^40+2012x^41+1580x^42+1388x^43+994x^44+564x^45+368x^46+140x^47+112x^48+4x^49+27x^50+11x^52+6x^54+2x^58

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 5.99 seconds.