The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+59x^34+188x^35+298x^36+498x^37+622x^38+866x^39+637x^40+462x^41+191x^42+88x^43+84x^44+62x^45+23x^46+10x^47+4x^48+2x^49+1x^62

The gray image is a linear code over GF(2) with n=312, k=12 and d=136.
This code was found by Heurico 1.16 in 0.203 seconds.