The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+133x^20+200x^21+560x^22+760x^23+1221x^24+1832x^25+2246x^26+2584x^27+2049x^28+1880x^29+1318x^30+744x^31+535x^32+184x^33+98x^34+8x^35+25x^36+2x^38+3x^40+1x^44

The gray image is a code over GF(2) with n=108, k=14 and d=40.
This code was found by Heurico 1.16 in 3.26 seconds.