The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+216x^57+373x^58+866x^59+889x^60+1244x^61+1167x^62+1570x^63+1207x^64+1594x^65+1267x^66+1534x^67+1020x^68+1150x^69+785x^70+654x^71+316x^72+278x^73+112x^74+72x^75+23x^76+22x^77+8x^78+8x^79+8x^81

The gray image is a code over GF(2) with n=260, k=14 and d=114.
This code was found by Heurico 1.13 in 4.42 seconds.