The generator matrix

 1  0  1  1  1  0  1  1  0  1  1 X+2  1  2  1  1  0  1  1  1  1  1  X  0  X X+2  X
 0  1  1  0  1  1  0 X+1  1  0 X+1  1  X  1  3 X+1  1  X  1  X X+3  X  2  1  X  1 X+2
 0  0  X  0  0  0  0  X  X X+2  2 X+2 X+2  X  X X+2 X+2 X+2  0  2 X+2  0  0  2  X  2  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  2  2  2 X+2  X  X X+2 X+2  2  X  X  2 X+2  X
 0  0  0  0  X X+2 X+2  X X+2  X  2 X+2  0  2  X  2  0  X  2  2  X  X  0 X+2  0  2  2
 0  0  0  0  0  2  0  0  2  0  2  0  2  2  2  0  2  0  2  2  0  0  2  2  0  2  0
 0  0  0  0  0  0  2  2  2  0  0  0  0  2  2  2  0  0  0  2  2  0  2  2  0  0  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+196x^20+72x^21+672x^22+576x^23+1579x^24+1424x^25+2630x^26+1960x^27+2746x^28+1512x^29+1592x^30+528x^31+631x^32+64x^33+160x^34+8x^35+26x^36+5x^40+2x^42

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 4.28 seconds.