The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  2  X  0  1  1  1  1  2
 0 2X+2  0  2  0  0  2  2 2X 2X  2 2X+2 2X+2 2X+2  0 2X  0  2 2X+2  0 2X+2 2X  2  2  2  2  0  0 2X 2X+2 2X+2  2  0  0  2  2 2X
 0  0 2X+2  2  0 2X+2 2X+2  0 2X  2  2  0 2X  2 2X 2X+2  0 2X+2  2 2X 2X  2  0  2  2 2X  0 2X+2 2X  0  0  0 2X 2X  2  2 2X
 0  0  0 2X  0  0 2X  0  0  0  0 2X 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0 2X  0
 0  0  0  0 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0 2X  0  0  0  0  0  0
 0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X  0 2X  0  0  0 2X 2X 2X 2X  0 2X 2X 2X  0  0 2X  0

generates a code of length 37 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+106x^32+116x^34+840x^36+740x^38+176x^40+28x^42+24x^44+12x^46+4x^48+1x^64

The gray image is a code over GF(2) with n=296, k=11 and d=128.
This code was found by Heurico 1.16 in 0.094 seconds.