The generator matrix

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

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+34x^30+64x^31+160x^32+202x^33+313x^34+598x^35+805x^36+1300x^37+1702x^38+1894x^39+2197x^40+1976x^41+1655x^42+1336x^43+815x^44+556x^45+350x^46+200x^47+103x^48+62x^49+31x^50+2x^51+11x^52+10x^54+2x^55+3x^56+1x^58+1x^60

The gray image is a code over GF(2) with n=160, k=14 and d=60.
This code was found by Heurico 1.16 in 6.9 seconds.