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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+50x^77+155x^78+146x^79+207x^80+288x^81+323x^82+406x^83+456x^84+542x^85+599x^86+712x^87+702x^88+588x^89+586x^90+606x^91+449x^92+294x^93+253x^94+206x^95+147x^96+110x^97+113x^98+70x^99+44x^100+32x^101+45x^102+24x^103+7x^104+14x^105+6x^106+6x^107+2x^108+2x^109+1x^132

The gray image is a linear code over GF(2) with n=352, k=13 and d=154.
This code was found by Heurico 1.16 in 8.36 seconds.