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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+225x^78+482x^80+28x^81+783x^82+168x^83+1044x^84+356x^85+1270x^86+644x^87+1581x^88+792x^89+1724x^90+948x^91+1557x^92+600x^93+1325x^94+396x^95+812x^96+140x^97+671x^98+20x^99+368x^100+4x^101+226x^102+139x^104+44x^106+31x^108+2x^110+2x^114+1x^128

The gray image is a linear code over GF(2) with n=360, k=14 and d=156.
This code was found by Heurico 1.16 in 32 seconds.