The generator matrix

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

generates a code of length 19 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+14x^13+147x^14+314x^15+477x^16+1082x^17+1174x^18+1774x^19+1172x^20+1122x^21+460x^22+278x^23+138x^24+22x^25+10x^26+2x^27+4x^28+1x^30

The gray image is a code over GF(2) with n=76, k=13 and d=26.
This code was found by Heurico 1.16 in 18.1 seconds.