The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+64x^55+183x^56+306x^57+400x^58+616x^59+799x^60+962x^61+1216x^62+1424x^63+1517x^64+1578x^65+1617x^66+1350x^67+1126x^68+958x^69+733x^70+516x^71+346x^72+248x^73+163x^74+112x^75+46x^76+40x^77+31x^78+12x^79+13x^80+4x^81+2x^83+1x^84

The gray image is a code over GF(2) with n=260, k=14 and d=110.
This code was found by Heurico 1.16 in 15.3 seconds.