The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+209x^62+360x^63+757x^64+424x^65+868x^66+536x^67+903x^68+568x^69+776x^70+472x^71+710x^72+352x^73+446x^74+200x^75+268x^76+120x^77+123x^78+32x^79+44x^80+8x^81+6x^82+5x^84+4x^86

The gray image is a code over GF(2) with n=276, k=13 and d=124.
This code was found by Heurico 1.13 in 1.35 seconds.