The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  1  X  X  X  1  X  1  1  1  1 X^2  1  1  1  X  1 X^2  1  X  X  1  1 X^2  1  X  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+85x^56+183x^60+46x^62+254x^64+424x^66+1143x^68+948x^70+550x^72+104x^74+162x^76+14x^78+100x^80+61x^84+17x^88+2x^92+1x^96+1x^108

The gray image is a linear code over GF(2) with n=276, k=12 and d=112.
This code was found by Heurico 1.16 in 2.02 seconds.