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  X  1  X  1  1  1  1  X  1  1  X  X  1  1  X  1  X  X  X  1  X  1  1  X  X  1  X  1  X  1  X  X  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  X  X  0  X  0  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  X  X  0  0  X  0  X  X  X  0  X  0  X  0  X  X  0  X  0  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  0  0  X  X  0  0  X  X  0  X  0  0  X  X  X  X  0  X  0  0  0  0  X  0  X  X  X  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  X  0  0  X  X  0  X  0  X  0  0  X  0  0  X  X  X  0  X  X  X  0  X  X  X  0  X  0  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  0  X  X  X  0  0  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  0  0  0  X  X  0  X  0  0  X  0  0  0  X  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  X  X  X  0  0  0  X  X  0  X  0  0  0  X  0  X  0  0  X  X  0  0  0  X  0  0  0  0  X  0  0  X  X  X  X  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  0  X  0  X  X  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  0  0  0  0  X  0  X  0  X  X  0  X  X  0  0  0  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  X  0  0  X  0  X  X  X  0  0  0  X  X  0  0  X  0  X  0  X  0  0  X  X  X  X  X  X  0  0  0  X  X  X  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  0  X  X  0  X  0  0  0  X  X  X  0  0  X  X  0  X  X  X  0  0  X  0  X  0  X  X  X  0  X  0  X  0  0  0  0  X  0  0  0  0  X  0  X  X  X  X
 0  0  0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  0  X  0  0  X  0  X  0  0  X  X  X  X  X  0  X  X  0  X  0  X  0  0  X  0  0  0  X  0  X  X  0  X  X  X  X  X  0  0  X  0  X  0  0  X  X  X  0
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  0  0  X  0  0  X  X  X  X  0  X  X  0  0  0  X  0  0  0  X  X  X  X  0  X  0  0  X  X  X  0  0  X  0  X  0  0  X  0  0  X  0  0  X  0
 0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  0  X  0  0  X  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  0  0  X  0  0  0  X  X  0  X  X  X  X  0

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+201x^48+600x^52+32x^54+1040x^56+374x^58+2015x^60+1280x^62+3021x^64+1510x^66+2701x^68+720x^70+1579x^72+162x^74+734x^76+16x^78+287x^80+2x^82+90x^84+12x^88+3x^92+2x^96+1x^100+1x^104

The gray image is a linear code over GF(2) with n=130, k=14 and d=48.
This code was found by Heurico 1.16 in 64.9 seconds.