The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+102x^20+52x^22+434x^24+560x^26+256x^27+1255x^28+768x^29+1336x^30+768x^31+1255x^32+256x^33+560x^34+434x^36+52x^38+102x^40+1x^60

The gray image is a code over GF(2) with n=120, k=13 and d=40.
This code was found by Heurico 1.16 in 1.61 seconds.