The generator matrix

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

generates a code of length 25 over Z2[X]/(X^4) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+212x^19+1324x^20+5008x^21+12757x^22+31608x^23+47783x^24+63614x^25+49522x^26+31676x^27+12340x^28+4724x^29+1137x^30+360x^31+54x^32+14x^33+8x^34+2x^36

The gray image is a linear code over GF(2) with n=200, k=18 and d=76.
This code was found by Heurico 1.16 in 152 seconds.