The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+37x^64+38x^65+103x^66+210x^67+278x^68+592x^69+498x^70+1042x^71+676x^72+1432x^73+1006x^74+1798x^75+1072x^76+1806x^77+913x^78+1546x^79+727x^80+1018x^81+402x^82+458x^83+223x^84+208x^85+102x^86+50x^87+46x^88+24x^89+34x^90+14x^91+10x^92+2x^93+6x^94+2x^95+1x^96+7x^98+1x^100+1x^110

The gray image is a linear code over GF(2) with n=304, k=14 and d=128.
This code was found by Heurico 1.16 in 18.8 seconds.