The generator matrix

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

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+46x^20+65x^22+28x^23+170x^24+116x^25+468x^26+444x^27+1094x^28+948x^29+1432x^30+948x^31+1095x^32+444x^33+480x^34+116x^35+138x^36+28x^37+102x^38+14x^40+12x^42+2x^44+1x^54

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 1.09 seconds.