The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 2 X 1 X 1 0 X 1 1 1 1 X
0 X 0 0 0 X X+2 X 2 2 X 0 0 X X X+2 2 0 X 2 X 2 X+2 X+2 2 X X X 0 X 0
0 0 X 0 X X X 0 2 0 X+2 X X+2 0 X+2 0 2 X+2 2 X X 0 X+2 2 2 0 X+2 X X X X
0 0 0 X X 0 X X+2 0 X 2 X 2 X+2 X 0 X+2 X 2 X+2 2 X+2 X 0 X X+2 0 0 X+2 X+2 X
0 0 0 0 2 0 0 0 2 2 2 2 0 2 0 2 0 0 0 2 0 0 2 2 0 2 2 0 0 2 0
0 0 0 0 0 2 0 2 0 0 0 2 2 0 2 0 2 2 2 0 0 2 2 2 0 2 2 0 0 0 2
generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 25.
Homogenous weight enumerator: w(x)=1x^0+44x^25+84x^26+116x^27+169x^28+208x^29+264x^30+344x^31+277x^32+150x^33+140x^34+94x^35+59x^36+44x^37+24x^38+20x^39+5x^40+2x^41+2x^43+1x^48
The gray image is a code over GF(2) with n=124, k=11 and d=50.
This code was found by Heurico 1.16 in 0.125 seconds.