The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+60x^62+616x^63+1325x^64+2014x^65+2950x^66+3366x^67+4123x^68+4148x^69+4252x^70+3494x^71+2752x^72+1610x^73+929x^74+558x^75+281x^76+136x^77+61x^78+42x^79+20x^80+12x^81+9x^82+4x^83+2x^84+3x^86

The gray image is a code over GF(2) with n=552, k=15 and d=248.
This code was found by Heurico 1.16 in 11.3 seconds.