The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+26x^20+81x^22+30x^23+111x^24+90x^25+162x^26+336x^27+521x^28+944x^29+1122x^30+1308x^31+1137x^32+916x^33+569x^34+352x^35+196x^36+96x^37+85x^38+22x^39+47x^40+2x^41+20x^42+9x^44+8x^46+1x^50

The gray image is a code over GF(2) with n=124, k=13 and d=40.
This code was found by Heurico 1.16 in 1.56 seconds.