The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  X  1  1  1  1  1  1  0  0  0  1  1  1  0  0  1  1  0  0  1  1  1  X  1  1  X  1  1  0  1  1  1  1  0  1  1  1  0  1  1  1  1  X  1  X  1  X  1  1  X  X  X  1  X  1  X
 0  1  1  0  1  1  0  1  1  0  1  1  X X+1  1  1  1  0  0  X X+1 X+1 X+1  1  1  1  0  0 X+1  1  1  0  0  1  1 X+1  X X+1  1 X+1  1  1  0  0  1  1  1  0  1  1  0  0  1  1 X+1  0 X+1  1  1  X  1  X  1  0  1  0  0  1  0  1 X+1  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  X  X  X  0  0  0  X  X  0  0  X  X  0  X  X  X  X  0  X  0  X  0  X  0  0  X  0  X  0  0  0  0  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  0  X  0  X  X  0  X  X  0  0  0  0  0  X  X  0  X  X  X  0  0  0  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  X  X  X  0  0  X  0  0  0  X  0  X  0  0  X  X  X  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  X  0  0  X  X  0  X  X  X  X  0  X  X  0  X  X  0  0  X  X  0  X  0  0  X  0  X  0  0  X  X  0  0  0  X  0  0  X  X  X  0  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  X  X  X  0  0  X  X  0  0  X  0  X  X  X  0  0  X  X  0  X  0  0  X  X  0  X  X  0  0  X  X  X  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  X  0  X  0  X  X  0  X  X  0  X  0  X  X  0  X  0  0  0  0  0  X  0  0  X  0  0  0  X  X  X  0  X  0  X  0  0  0  X  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  X  X  0  0  X  0  X  X  X  X  0  0  X  0  X  0  X  0  X  0  0  0  X  0  0  0  0  X  0  0  X  0  0  X  X  0  X  X  0  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  X  0  0  0  X  X  X  X  X  X  0  X  0  0  X  0  0  X  X  X  0  0  X  0  0  X  X  X  X  X  0  0  X  X  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  0  0  X  X  X  X  0  0  X  X  X  0  X  X  0  0  0  X  0  0  X  0  0  X  0  X  X  0  0  X  X  0  0  0  X  X  0  X  0  X  0  X  0  0  X  X  0  0  0  0  0  X  X  0  0  X
 0  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  0  X  X  0  X  X  X  0  0  X  X  X  X  X  0  X  X  0  X  X  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  X  X  0  0  0  X  X  X  X  X  0  0  X  X  X  0  X  X
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  0  X  0  X  X  X  X  0  0  0  0  X  X  X  0  X  0  0  0  X  X  0  X  0  0  0  0  X  X  X  X  0  X  0  0  0  0  0  0  X  X  0  X  X  X  X  X  0  X  0  0  X  X  0

generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+147x^56+14x^58+561x^60+268x^62+1253x^64+922x^66+2037x^68+1712x^70+2495x^72+1762x^74+2049x^76+1116x^78+1073x^80+310x^82+430x^84+40x^86+146x^88+42x^92+5x^96+1x^116

The gray image is a linear code over GF(2) with n=144, k=14 and d=56.
This code was found by Heurico 1.16 in 51.9 seconds.