The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+50x^30+199x^32+32x^33+378x^34+128x^35+704x^36+320x^37+1080x^38+544x^39+1326x^40+544x^41+1108x^42+320x^43+677x^44+128x^45+402x^46+32x^47+133x^48+50x^50+26x^52+4x^54+4x^56+1x^60+1x^64

The gray image is a code over GF(2) with n=160, k=13 and d=60.
This code was found by Heurico 1.16 in 2.8 seconds.