The generator matrix

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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+59x^28+70x^29+168x^30+214x^31+354x^32+528x^33+598x^34+744x^35+905x^36+1142x^37+1223x^38+1414x^39+1463x^40+1304x^41+1385x^42+1208x^43+922x^44+858x^45+582x^46+442x^47+314x^48+184x^49+128x^50+64x^51+65x^52+10x^53+11x^54+10x^55+11x^56+1x^58+1x^60+1x^64

The gray image is a linear code over GF(2) with n=80, k=14 and d=28.
This code was found by Heurico 1.16 in 31.6 seconds.