The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  X  1  0  X  X  X  1  1  1  1
 0  X  0  0  0  X X+2  X  0  2  2  X X+2  0  0  0  X  X  X  2  X X+2  X  2 X+2 X+2  2
 0  0  X  0  X  X X+2  0  0  0  X  X X+2  2  X  X  2  2  2  0  X  X  0 X+2  X X+2  0
 0  0  0  X  X  0 X+2  X  2  X  2  0 X+2 X+2  X X+2  2  X  0  X  2  X  X  0  X  0  2
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  2  0  2  2  2  2  2  2  2  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  2  0  0  2  2  2  0  2  0  2  0  2  2  2  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  0  0  2  0  0  0  2  2  0  2  0  0  2  2
 0  0  0  0  0  0  0  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  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+208x^20+426x^22+112x^23+889x^24+528x^25+1430x^26+800x^27+1747x^28+480x^29+858x^30+112x^31+427x^32+16x^33+98x^34+52x^36+4x^38+3x^40+1x^44

The gray image is a code over GF(2) with n=108, k=13 and d=40.
This code was found by Heurico 1.16 in 1.51 seconds.