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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+78x^75+140x^76+148x^77+171x^78+214x^79+301x^80+286x^81+306x^82+298x^83+332x^84+416x^85+291x^86+234x^87+199x^88+146x^89+123x^90+90x^91+72x^92+70x^93+56x^94+38x^95+31x^96+16x^97+7x^98+6x^99+11x^100+6x^101+6x^102+2x^103+1x^124

The gray image is a linear code over GF(2) with n=336, k=12 and d=150.
This code was found by Heurico 1.16 in 3.31 seconds.