The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  X  1  1  1  1  X  X  0  1  1  X  1  0  0  1  X  1  X  1  X  1  1  X  1  1  1  0  1  1  0  1  1  X  0  X  0  X  1  1  0  1  0  1  0  1  1  1  0  1  1  1  1  1  X  X  1  X  1  1  1  1  0
 0  1  0  1  0  1  1  0  0  1 X+1  1  X  1  0  X X+1  1  1  1  0 X+1  0  1  0  1  0  0  X  1  1  X  1  0 X+1  1  X  0  1  0  1 X+1  1  1  X  1  1  1  X  1 X+1  0  1  0  1  X  1  1  X  X  1 X+1 X+1 X+1  X X+1  0  1 X+1  X  X X+1  X  X  X
 0  0  1  1  1  0  1  0  1  1  0  X  1 X+1 X+1  X  0 X+1  X X+1  1 X+1  X X+1 X+1  X  1  X  1  X  1  1  1  X X+1  0  X  0  0  1  1  1  X X+1  1  1  1  X  1  0  X  1  X X+1  X  X  1  1 X+1  1  1 X+1  X  X  1 X+1  1  0  X  1  1  X  0  X  1
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  0  0  0  X  0  0  X  X  0  X  0  X  X  0  0  X  X  0  0  X  0  X  X  0  0  0  X  X  0  X  0  0  X  X  0  0  X  X  X  X  X  0  0  X  X  X  X  0  X  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  0  0  0  X  X  0  0  X  0  X  X  X  X  0  X  X  X  X  0  0  0  X  X  0  0  X  0  0  X  X  0  0  0  0  X  X  0  X  X  X  X  X  0  X  X  0  0  X  0  X  X  X  0  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  0  0  X  0  X  0  X  X  0  0  0  X  X  X  X  0  X  0  X  X  X  X  0  X  X  0  X  X  X  X  X  0  0  X  0  X  0  0  X  0  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  0  0  X  0  X  0  X  X  0  X  X  X  0  X  0  0  X  X  X  0  0  X  X  X  0  X  X  X  X  X  0  X  0  X  X  0  X  X  0  X  0  0  X  0  X  0  0  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  0  0  0  0  X  0  0  0  X  X  0  X  X  X  X  X  0  X  0  X  X  0  X  X  0  0  0  0  X  X  X  X  X  X  0  0  0  X  0  0  X  0  0  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  0  0  X  X  0  0  X  X  X  0  X  X  X  0  0  X  X  0  X  X  0  0  X  X  0  X  X  0  X  X  0  X  0  0  X  0  0  0  0  0  0  0  X  X  0  0  X  X  0  0  0  0  X  X  0  X  X  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  0  X  X  0  X  X  0  X  0  0  0  X  X  X  X  X  0  X  X  0  X  0  0  X  X  X  0  0  X  0  0  0  0  X  0  0  X  0  X  0  X  0  X  0  X  0  0  X  0  X  X  X  X  X  0  X  0

generates a code of length 75 over Z2[X]/(X^2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+65x^62+58x^63+157x^64+198x^65+226x^66+252x^67+339x^68+322x^69+376x^70+474x^71+419x^72+504x^73+465x^74+532x^75+499x^76+476x^77+504x^78+390x^79+349x^80+398x^81+254x^82+268x^83+174x^84+130x^85+121x^86+70x^87+74x^88+20x^89+29x^90+4x^91+27x^92+5x^94+7x^96+2x^98+1x^100+1x^102+1x^104

The gray image is a linear code over GF(2) with n=150, k=13 and d=62.
This code was found by Heurico 1.16 in 12.9 seconds.