The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+47x^44+78x^45+108x^46+136x^47+168x^48+218x^49+219x^50+220x^51+212x^52+178x^53+126x^54+102x^55+57x^56+46x^57+45x^58+32x^59+19x^60+8x^61+11x^62+6x^63+8x^64+2x^66+1x^78

The gray image is a code over GF(2) with n=204, k=11 and d=88.
This code was found by Heurico 1.16 in 0.261 seconds.