The generator matrix

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

generates a code of length 19 over Z2[X]/(X^4) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+150x^15+169x^16+528x^17+600x^18+1206x^19+632x^20+544x^21+96x^22+114x^23+30x^24+16x^25+8x^26+2x^27

The gray image is a linear code over GF(2) with n=152, k=12 and d=60.
This code was found by Heurico 1.16 in 71.4 seconds.