The generator matrix

 1  0  0  1  1  1 X^3+X  1  1  1  1  1  1 X^2  1
 0  1  0  X X^2+1 X^3+X+1  1 X^2 X^2+X+1 X^3+X  1  1 X^2+1  1  0
 0  0  1  1 X+1  0  1 X^2+X  X X^2+X+1 X+1  X X^2 X^2+X  0
 0  0  0 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3

generates a code of length 15 over Z2[X]/(X^4) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+82x^11+494x^12+1522x^13+3246x^14+5648x^15+3367x^16+1480x^17+428x^18+94x^19+10x^20+6x^21+6x^22

The gray image is a linear code over GF(2) with n=120, k=14 and d=44.
This code was found by Heurico 1.16 in 0.453 seconds.