The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+43x^60+150x^61+218x^62+344x^63+451x^64+494x^65+669x^66+690x^67+681x^68+760x^69+767x^70+728x^71+604x^72+512x^73+383x^74+238x^75+166x^76+114x^77+58x^78+32x^79+24x^80+18x^81+11x^82+14x^83+13x^84+3x^86+1x^90+2x^91+1x^92+2x^94

The gray image is a code over GF(2) with n=276, k=13 and d=120.
This code was found by Heurico 1.16 in 4.83 seconds.