The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  1  0  0  1  X  0  1  1  1  1  1  0  0  1  0  X  1  X  1  X  X  X  1  X  1  1  1  X  1  0  1  1  0  X  X  0  1  1  1  0  0  0  1  X  1  1  1  1  1  1  0  X  1  X  1  1
 0  1  0  1  0  1  1  0  0  1  1  1  1  0 X+1  0  X  0  1  1  1  X  0  X  1  0  0  1  1  1  X  1  1  1  0  0  1  0  1  1  X X+1  X  1  1  1 X+1  1  1  1  1  X  X  1  X  1  1  1  1  1  1 X+1 X+1  X X+1  0  1  1  1  0  0  0
 0  0  1  1  1  0  1  0  1  1  0  X X+1  1  0  0  1  1  0  1  1  1  0  1 X+1  1  0  X X+1  X  1  X  1  1 X+1  1  X  1 X+1  0  0  X  0  1  X  1  X X+1  1  0  X  1  1  X  1  1 X+1  1 X+1  0 X+1 X+1  1  1  1 X+1  0  1  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  X  X  0  X  X  0  0  X  0  X  X  X  0  X  X  0  X  0  0  X  X  0  X  X  X  0  0  0  X  0  X  X  X  X  0  0  X  0  X  X  X  X  0  0  X  0  0  X  0  X  0  X  0  X  0  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  0  0  X  X  X  X  X  X  X  X  0  X  X  X  0  0  X  0  X  0  X  0  X  X  0  0  X  0  X  0  0  0  X  0  X  0  X  X  X  X  0  0  X  0  0  0  X  0  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  0  0  X  X  0  0  X  X  X  0  X  0  0  X  X  X  0  X  0  0  X  X  0  X  0  0  0  X  X  X  0  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  X  0  0  X  0  X  0  0  0  X  0  X  0  0  0  X  X  X  X  0  X  0  0  0  X  X  0  X  0  X  X  X  X  X  X  0  X  0  0  X  X  0  X  0  X  X  X  0  0  0  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  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  X  X  0  0  X  X  X  0  0  X  X  0  X  X  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  X  0  X  0  X  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  0  0  X  0  0  X  X  X  X  0  X  0  X  0  X  0  X  0  X  0  0  X  X  0  0  X  X  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  X  X  X  X  X  X  X  0  X  X  0  X  0  0  0  0  X  0  X  X  X  0  X  X  0  X  X  X  X  X  X  X  0  0  X  X  X  0  X  0  X  X  0  X  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  X  0  0  0  0  0  X  0  X  X  0  0  0  X  X  X  X  0  0  X  0  0  X  X  X  X  0  0  X  0  0  X  X  X  X  0  X  X  X  X  0  0  X  X  X  0  0  0  0  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+58x^56+162x^58+423x^60+660x^62+1004x^64+1247x^66+1643x^68+1928x^70+2021x^72+2071x^74+1684x^76+1325x^78+932x^80+591x^82+351x^84+154x^86+63x^88+36x^90+11x^92+13x^94+1x^96+4x^98+1x^106

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 44.1 seconds.