The generator matrix

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

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+55x^16+24x^17+200x^18+164x^19+481x^20+610x^21+1021x^22+1368x^23+1948x^24+2538x^25+2930x^26+3512x^27+3177x^28+3396x^29+2775x^30+2592x^31+2023x^32+1468x^33+1076x^34+516x^35+467x^36+154x^37+171x^38+40x^39+36x^40+2x^41+18x^42+3x^44+1x^46+1x^48

The gray image is a linear code over GF(2) with n=56, k=15 and d=16.
This code was found by Heurico 1.16 in 22.8 seconds.