The generator matrix

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

generates a code of length 36 over Z2[X]/(X^4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+416x^31+1047x^32+2964x^33+3242x^34+6166x^35+5181x^36+6308x^37+3252x^38+2714x^39+834x^40+432x^41+122x^42+62x^43+17x^44+8x^45+2x^47

The gray image is a linear code over GF(2) with n=288, k=15 and d=124.
This code was found by Heurico 1.16 in 6.13 seconds.