The generator matrix

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

generates a code of length 19 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+167x^16+556x^17+768x^18+1216x^19+681x^20+512x^21+136x^22+16x^23+38x^24+4x^25+1x^28

The gray image is a linear code over GF(2) with n=152, k=12 and d=64.
This code was found by Heurico 1.16 in 0.125 seconds.